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+{
+ "metadata": {
+  "name": "chapter12.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 12: Kinematics of a Particle"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Ex 12.12-1, Page No 200"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "# Initilization of variables\n",
+      "t=4 #seconds\n",
+      "\n",
+      "# Calculations\n",
+      "#Displacement \n",
+      "x=3*t**3+t+2 #ft\n",
+      "# Velocity\n",
+      "v=9*t**2+1 # ft/s\n",
+      "# Acceleration\n",
+      "a=18*t # ft/s**2\n",
+      "\n",
+      "# Result\n",
+      "print'The dipalacemnt is',round(x),\"ft\"\n",
+      "print'The velocity is ',round(v),\"ft/s\"\n",
+      "print'The acceleration is ',round(a),\"ft/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The dipalacemnt is 198.0 ft\n",
+        "The velocity is  145.0 ft/s\n",
+        "The acceleration is  72.0 ft/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-2, Page No 201"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "# Initilization of variables\n",
+      "t1=4 #s\n",
+      "t2=5 #s\n",
+      "\n",
+      "# Calculation\n",
+      "v1=9*t1**2+1 # ft/s\n",
+      "v2=9*t2**2+1 # ft/s\n",
+      "a=(v2-v1)/(t2-t1) # m/s**2\n",
+      "\n",
+      "# Result\n",
+      "print'The acceleration during fifth second is',round(a),\"ft/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The acceleration during fifth second is 81.0 ft/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-3, Page No 201"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Defining Matrices\n",
+      "t=[0,1,2,3,4,5,10] #s\n",
+      "# equation for s is s=8*t**2+2*t, Thus the different values of s corresponding to t is:\n",
+      "#Displacement matrix\n",
+      "s=[0,10,36,78,136,210,820]\n",
+      "# Eqn for v is v=16*t+2,Thus the different values of v corresponding to t is:\n",
+      "#Velocity Matrix\n",
+      "v=[0,18,34,50,66,82,162]\n",
+      "# Eqn for a is a=16, Thus the different values of a corresponding to t is:\n",
+      "#Acceleration Matrix\n",
+      "a=[16,16,16,16,16,16,16]\n",
+      "#Plotting the curves\n",
+      "#S-T curve\n",
+      "plot(t,s)\n",
+      "plot(t,v)\n",
+      "plot(t,a)\n",
+      "xlabel('t(s)')\n",
+      "ylabel('s(m), v(m/s) & a(m/s**2)')\n",
+      "\n",
+      "#Result\n",
+      "print'The graphs are the solutions'\n",
+      "print'blue line is for \"s\" vs \"t\" '\n",
+      "print'green line is for \"v\" vs \"t\" '\n",
+      "print'red line is for \"a\" vs \"t\" '\n",
+      "# All the 3 graphs have been combined into a single graph"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The graphs are the solutions\n",
+        "blue line is for \"s\" vs \"t\" \n",
+        "green line is for \"v\" vs \"t\" \n",
+        "red line is for \"a\" vs \"t\" \n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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6dOlyx8E2hSQHIepWVaVWVI2PVxODwaB1RMIaNHty+OSTT5g2bRqdrWTOmyQH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\ngxBCiBokOQghhKhBkoMQQoga/j9a1TbNrs4KNwAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x594d050>"
+       ]
+      }
+     ],
+     "prompt_number": 31
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example No 12.12-4, Page No 202"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "v_o=0 #ft/s\n",
+      "v_f=88#ft/s\n",
+      "t=28 #s\n",
+      "\n",
+      "#Calculations\n",
+      "k=(v_f-v_o)*t**-1 #ft/s**2\n",
+      "s=((v_f-v_o)/2)*t #ft\n",
+      "\n",
+      "#Result\n",
+      "print'The value of constant k is',round(k,2),\"ft/s**2\"\n",
+      "print'The displacement is ',round(s),\"ft\"\n",
+      "#Decimal accuracy causes discrepancy in answers\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The value of constant k is 3.14 ft/s**2\n",
+        "The displacement is  1232.0 ft\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-5, Page No 202"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "v_o=0 #ft/s\n",
+      "v_f1=30 #ft/s\n",
+      "v_f2=0 #ft/s\n",
+      "t1=3 #s\n",
+      "t2=2 #s\n",
+      "\n",
+      "#Calculations\n",
+      "#Plotting the v-t curve\n",
+      "#Velocity matrix \n",
+      "v=[v_o,v_f1,v_f2]\n",
+      "#Time matrix\n",
+      "t=[0,3,5]\n",
+      "plot(t,v)\n",
+      "xlabel('t')\n",
+      "ylabel('v')\n",
+      "#Part \"b\"\n",
+      "#Acceleration at 3s\n",
+      "a1=(v_f1-v_o)/t1 #ft/s**2\n",
+      "#Acceleration at 5s\n",
+      "a2=(v_f2-v_f1)/t2 #ft/s**2\n",
+      "#Part \"c\"\n",
+      "s=(v_f1*t1*0.5)+(v_f1*t2*0.5) #ft\n",
+      "#Part \"d\"\n",
+      "#Simplfying the equation we get\n",
+      "#7.5t**2-30t+5=0\n",
+      "a=7.5\n",
+      "b=-30\n",
+      "c=5\n",
+      "q=sqrt(b**2-4*a*c)\n",
+      "x1=(-b+q)/(2*a)\n",
+      "x2=(-b-q)/(2*a)\n",
+      "#As x1 is greater than 2 it does not hold as a solution\n",
+      "t=x2 #s\n",
+      "#Hence total time is\n",
+      "T=t1+t #s\n",
+      "\n",
+      "#Result\n",
+      "print'The graph is the solution for part a'\n",
+      "print'The acceleration at 3rd second is',round(a1),\"ft/s**2\"\n",
+      "print'The acceleration at 5th second is',round(a2),\"ft/s**2\"\n",
+      "print'The displacement is',round(s),\"ft\"\n",
+      "print'The total time is',round(T,3),\"s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The graph is the solution for part a\n",
+        "The acceleration at 3rd second is 10.0 ft/s**2\n",
+        "The acceleration at 5th second is -15.0 ft/s**2\n",
+        "The displacement is 75.0 ft\n",
+        "The total time is 3.174 s\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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+       "text": [
+        "<matplotlib.figure.Figure at 0x594d2d0>"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example No 12.12-6, Page No 203"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "v_o=2 #m/s\n",
+      "y_o=120 #m\n",
+      "g=9.8 #m/s**2\n",
+      "\n",
+      "#Calculations\n",
+      "#Solve  using ground as datum\n",
+      "y=0\n",
+      "#Simplfying the equation\n",
+      "a=4.9\n",
+      "b=-2\n",
+      "c=-120\n",
+      "q=sqrt(b**2-4*a*c)\n",
+      "x1=(-b+q)/(2*a) #s\n",
+      "x2=(-b-q)/(2*a) #s\n",
+      "\n",
+      "#Result\n",
+      "print'The time required is',round(x1,2),\"s\"\n",
+      "#As x2 is negative and negative time does not make any physical sense\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The time required is 5.16 s\n"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-7, Page No 204"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "Vo1=80 #ft/s\n",
+      "Vo2=60 #ft/s\n",
+      "g=32.2 #ft/s**2\n",
+      "\n",
+      "#Calculations\n",
+      "#Simplfying by equating the two times\n",
+      "t=(-(Vo2*2)-(g*0.5*4))/(Vo1-Vo2-(g*0.5*4)) #s\n",
+      "#Substituting this t in s we get\n",
+      "s=(Vo1*t)-(0.5*g*t*t) #ft\n",
+      "\n",
+      "#Result\n",
+      "print'The time obtained is',round(t,2),\"s\"\n",
+      "print'and the ball meets at',round(s,1),\"ft\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The time obtained is 4.15 s\n",
+        "and the ball meets at 54.5 ft\n"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-8, Page No 204"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "# as theta=40 degrees\n",
+      "costheta=0.77\n",
+      "tantheta=0.83\n",
+      "x=100 #ft\n",
+      "ay=32.2 #ft/s**2\n",
+      "\n",
+      "#Calculations\n",
+      "#Simplfying the equation\n",
+      "t=((tantheta*x)*(ay/2)**-1)**0.5 #s\n",
+      "#Velocity calculations\n",
+      "Vo=100*(costheta*t)**-1 #ft/s\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print'The initial speed should be',round(Vo,1),\"ft/s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The initial speed should be 57.2 ft/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 24
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-9, Page No 204"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=[0,1,2,3,4,5,6] #s\n",
+      "#Solving the Differential Equations we obtain\n",
+      "# Eqn for s is s=(t+1)**3,Thus the different values of s corresponding to t is:\n",
+      "#Displacement matrix\n",
+      "s=[1,8,27,64,125,216,343]\n",
+      "# Eqn for v is v=3*(t+1)**2, Thus the different values of v corresponding to t is:\n",
+      "# Velocity matrix\n",
+      "v=[3,12,27,48,75,108,147]\n",
+      "# Eqn for a is a=6*(t+1),Thus the different values of a corresponding to t is:\n",
+      "# Acceleration matrix\n",
+      "a=[6,12,18,24,30,36,42]\n",
+      "#Plotting\n",
+      "plot(t,s)\n",
+      "plot(t,v)\n",
+      "plot(t,a)\n",
+      "xlabel('t(s)')\n",
+      "ylabel('s(ft) , v(ft/s) & a(ft/s**2)')\n",
+      "\n",
+      "#Result\n",
+      "print'The result are the plots that have been generated'\n",
+      "print'blue line is for \"s\" vs \"t\"'\n",
+      "print'green line is for \"v\" vs \"t\"'\n",
+      "print'red line is for \"a\" vs \"t\"'\n",
+      "# All the graphs have been plotted on a single graph"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The result are the plots that have been generated\n",
+        "blue line is for \"s\" vs \"t\"\n",
+        "green line is for \"v\" vs \"t\"\n",
+        "red line is for \"a\" vs \"t\"\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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1a9WFbkTpnE84z4rjK/jxrx8Z22Ess3rOop1DuwqNoSTXTqlOLoQoUkEBLF8O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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x58313f0>"
+       ]
+      }
+     ],
+     "prompt_number": 32
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-10, Page No 205"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=3 #s\n",
+      "\n",
+      "#Calculations\n",
+      "#After solving the differential equation\n",
+      "s=(3**-1)*(t+2)**3 #ft\n",
+      "v=(t+2)**2 #ft/s\n",
+      "a=2*(t+2) #ft/s**2\n",
+      "\n",
+      "#Result\n",
+      "print'The displacement at t=3s is',round(s,1),\"ft\"\n",
+      "print'The velocity at t=3s is',round(v),\"ft/s\"\n",
+      "print'The acceleration at t=3s is',round(a),\"ft/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The displacement at t=3s is 41.7 ft\n",
+        "The velocity at t=3s is 25.0 ft/s\n",
+        "The acceleration at t=3s is 10.0 ft/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 33
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-12, Page No 206"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "#Calling upward direction positive\n",
+      "xdot1=6 #ft/s\n",
+      "xdot3=3 #ft/s\n",
+      "xdoubledot=2 #ft/s**2\n",
+      "xdoubledot3=-4 #ft/s**2\n",
+      "\n",
+      "#Calculations\n",
+      "xdot=-xdot1 #ft/s\n",
+      "xdot2=2*xdot-xdot3 #ft/s\n",
+      "xdoubledot2=2*xdoubledot-xdoubledot3 #ft/s**2\n",
+      "\n",
+      "#Result\n",
+      "print'The value of velocity is',round(xdot2,3),\"ft/s (down)\"\n",
+      "print'The value of acceleration is',round(xdoubledot2,3),\"ft/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The value of velocity is -15.0 ft/s (down)\n",
+        "The value of acceleration is 8.0 ft/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 35
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-16, Page No 207"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=4 #s\n",
+      "\n",
+      "#Calculations\n",
+      "#Part (a)\n",
+      "x=t**3 #in\n",
+      "y=-2*t**2 #in\n",
+      "z=2*t #in\n",
+      "#Part (b)\n",
+      "#Theory question\n",
+      "#Part(c)\n",
+      "#Unit vector calculation\n",
+      "m=(4**2+1**1+(-3)**2)**0.5\n",
+      "e_l=[4*m**-1,m**-1,-3*m**-1]\n",
+      "v=[3*t**2,-4*t,2] #in/s\n",
+      "#Projection of v on n at t=4s\n",
+      "dot=[v[0]*e_l[0],v[1]*e_l[1],v[2]*e_l[2]]\n",
+      "#dot=v.*e_l #in/s\n",
+      "a=dot[0]+dot[1]+dot[2] #in/s\n",
+      "\n",
+      "#Result\n",
+      "print'The co-ordinates of position are x=',round(x),\"in ,\",round(y),\"in and \",round(z),\"in respectively\"\n",
+      "print'The projection of v on n at t=4s is',round(a,1),\"in/s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The co-ordinates of position are x= 64.0 in , -32.0 in and  8.0 in respectively\n",
+        "The projection of v on n at t=4s is 33.3 in/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 39
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-17, Page No 208"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "theta=pi/3 #rad\n",
+      "\n",
+      "#Calculations\n",
+      "#Method (a)\n",
+      "t=(theta)**0.5 #s\n",
+      "r=2*theta\n",
+      "rdot=4*t\n",
+      "thetadot=2*t\n",
+      "#Velocity calculations\n",
+      "x=r*thetadot\n",
+      "v=((rdot)**2+x**2)**0.5 #ft/s\n",
+      "#Theta calculations\n",
+      "thetax=30+arctan(rdot/x)*(180/pi) #degrees\n",
+      "#Method (b)\n",
+      "x=2*theta*cos(theta) #ft\n",
+      "y=2*theta*sin(theta) #ft\n",
+      "xdot=4*t*((cos(t**2)))+2*t**2*(-sin(t**2))*(2*t) #ft/s\n",
+      "ydot=4*t**2*sin(t**2)+2*t**2*cos(t**2)*2*t #ft/s\n",
+      "V=(xdot**2+ydot**2)**0.5 #ft/s\n",
+      "Thetax=arctan(ydot/-xdot)*(180/pi) #degrees\n",
+      "\n",
+      "#Result\n",
+      "print'By both the methods we obtain v and thetax as:'\n",
+      "print'Method 1'\n",
+      "print'v=',round(v,2),\"ft/s\",'and thetax=',round(thetax,1),\"degrees\"\n",
+      "print'Method 2'\n",
+      "print'V=',round(v,2),\"ft/s\",'and Thetax=',round(Thetax,1),\"degrees\"\n",
+      "# The answer may wary due to decimal point accuracy"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "By both the methods we obtain v and thetax as:\n",
+        "Method 1\n",
+        "v= 5.93 ft/s and thetax= 73.7 degrees\n",
+        "Method 2\n",
+        "V= 5.93 ft/s and Thetax= 73.9 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 76
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-18, Page No 209"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "theta=pi/3 #rad\n",
+      "\n",
+      "#Calculations\n",
+      "t=sqrt(theta) #s\n",
+      "thetadot=2*t \n",
+      "thetadoubledot=2\n",
+      "r=2*t**2\n",
+      "rdot=4*t\n",
+      "rdoubledot=4\n",
+      "ax=rdoubledot-(r*thetadoubledot*thetadoubledot) #ft/s**2\n",
+      "ay=2*rdot*thetadot+r*thetadoubledot #ft/s**2\n",
+      "a=sqrt(ax**2+ay**2) # fr/s**2\n",
+      "thetax=30+arctan(ax/ay)*(180/pi) #degrees\n",
+      "#Solving by cartesian co-ordinate system yields same solution\n",
+      "\n",
+      "#Result\n",
+      "print'The value of acceleration is',round(a,1),\"ft/s**2\"\n",
+      "print'The value of thetax is',round(thetax,1),\"degrees\"\n",
+      "#Decimal accuracy causes discrepancy in answers\n",
+      "# The ans for thetax is incorrcet in textbook"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The value of acceleration is 21.4 ft/s**2\n",
+        "The value of thetax is 18.2 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 78
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-21, Page No 211"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "Va=5 #ft/s\n",
+      "# as theta=70 degrees\n",
+      "sintheta=0.94\n",
+      "costheta=0.34\n",
+      "l=6.24 #ft\n",
+      "\n",
+      "#Calculations\n",
+      "Vb=(-costheta/sintheta)*Va #ft/s\n",
+      "\n",
+      "#Result\n",
+      "print'The value of Vb is',round(Vb,2),\"ft/s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The value of Vb is -1.81 ft/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 81
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.25-25, Page No 214"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "import numpy as np\n",
+      "\n",
+      "#Initilization of variables\n",
+      "theta=linspace(0,360,13)\n",
+      "\n",
+      "#Calculations\n",
+      "#Defining everything in terms of matrices \n",
+      "t=(theta*pi)/(180) #s converting degrees to radians\n",
+      "costheta=cos(t) \n",
+      "sintheta=sin(t)\n",
+      "x=2*costheta #ft\n",
+      "v=-12*sintheta #ft/s\n",
+      "a=-72*costheta #ft/s**2\n",
+      "\n",
+      "#Plotting\n",
+      "# 1\n",
+      "plot(t,x)\n",
+      "# 2\n",
+      "plot(t,v)\n",
+      "# 3\n",
+      "plot(t,a)\n",
+      "xlabel('t(s)')\n",
+      "ylabel('x(ft) , v(ft/s) ,a(ft/s**2)')\n",
+      "\n",
+      "#Result\n",
+      "print'The results are the plots'\n",
+      "print'The curve in blue colour represents t vs x'\n",
+      "print'The curve in green represents t vs v'\n",
+      "print'The curve in red represents t vs a'\n",
+      "# All the 3 curves have been plotted in the same graph. "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The results are the plots\n",
+        "The curve in blue colour represents t vs x\n",
+        "The curve in green represents t vs v\n",
+        "The curve in red represents t vs a\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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9jtmdU9i1axczZ87UDx+FhYVha2tb7GSzjY0NqTdSWX5sOZFxkexL2scQzyH6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\nhBBCT4qCEEIIvf8HaEMe+5zwRtYAAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x5e5d030>"
+       ]
+      }
+     ],
+     "prompt_number": 29
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-26, Page No 215"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "d=1.2 #m\n",
+      "w0=0 #rpm\n",
+      "w=2000 #rpm\n",
+      "t=20 #s\n",
+      "\n",
+      "#Calculations\n",
+      "alpha=(w-w0)/t \n",
+      "alpha_rad=(alpha*2*pi)/60 #converting to radians/s**2\n",
+      "\n",
+      "#Result\n",
+      "print'The angular acceleration is',round(alpha_rad,1),\"radians/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The angular acceleration is 10.5 radians/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-27, Page No 216"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "w0=0 #rad/s\n",
+      "w=209 #rad/s\n",
+      "t=20 #s\n",
+      "\n",
+      "#Calculations\n",
+      "theta=0.5*(w+w0)*t #rad\n",
+      "theta_rev=round(theta/(2*pi)) #revolutions rounding off\n",
+      "\n",
+      "#Result\n",
+      "print'The flywheel makes',round(theta_rev),\"revolutions\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The flywheel makes 333.0 revolutions\n"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-28, Page No 216"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "w0=0 #rad/s\n",
+      "alpha=10.5 #rad/s**2\n",
+      "t=0.6 #s\n",
+      "r=0.6 #m\n",
+      "\n",
+      "#Calculations\n",
+      "w=w0+alpha*t #rad/s\n",
+      "v=r*w #m/s\n",
+      "a_t=r*alpha #m/s**2\n",
+      "a_n=r*w*w #m/s**2\n",
+      "a=sqrt(a_t**2+a_n**2) #m/s**2\n",
+      "phi=arctan(a_t/a_n)*(180/pi) #degrees\n",
+      "\n",
+      "#result\n",
+      "print'The tangential velocity is',round(v,2),\"m/s\"\n",
+      "print'The acceleration is',round(a,1),\"m/s**2\"\n",
+      "print'and the angle is',round(phi,1),\"degrees\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The tangential velocity is 3.78 m/s\n",
+        "The acceleration is 24.6 m/s**2\n",
+        "and the angle is 14.8 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-29, Page No 216"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "l=4 #ft\n",
+      "wb=40 #rpm\n",
+      "we=60 #rpm\n",
+      "\n",
+      "#Calculations\n",
+      "r=l/2 #ft\n",
+      "vb=r*((wb*2*pi)/60) #ft/s\n",
+      "ve=r*((we*2*pi)/60) # ft/s\n",
+      "\n",
+      "#Result\n",
+      "print'The linear speeds are:'\n",
+      "print'vb=',round(vb,2),\"ft/s\"\n",
+      "print'and ve=',round(ve,1),\"ft/s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The linear speeds are:\n",
+        "vb= 8.38 ft/s\n",
+        "and ve= 12.6 ft/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-30, Page No 217"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "wb=40 #rpm\n",
+      "we=60 #rpm\n",
+      "t1=5 #s using different symbol to avoid conflict in decleration\n",
+      "t=2 #s\n",
+      "#Calculations\n",
+      "\n",
+      "alpha=(((we*2*pi)/60)-((wb*2*pi)/60))/t1 #rad/s**2\n",
+      "w=((wb*2*pi)/60)+alpha*t #rad/s\n",
+      "#Components of acceleration are\n",
+      "a_t=r*alpha #ft/s**2\n",
+      "a_n=r*w**2 #ft/s**2\n",
+      "\n",
+      "#result\n",
+      "print'The tangential acceleration is',round(a_t,3),\"ft/s**2\"\n",
+      "print'The normal acceleration is',round(a_n,1),\"ft/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The tangential acceleration is 0.838 ft/s**2\n",
+        "The normal acceleration is 50.5 ft/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 23
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-31, Page No 217"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "d=200 #mm\n",
+      "w0=(800*2*pi)/60 #rpm\n",
+      "w=0 #rpm\n",
+      "t=600 #s\n",
+      "\n",
+      "#Calculations\n",
+      "alpha=(w-w0)/t #rad/s**2 (deceleration)\n",
+      "\n",
+      "#result\n",
+      "print'The angular acceleration is',round(alpha,2),\"radian/s**2\"\n",
+      "# The negative sign indicates that the wheel decelerates\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The angular acceleration is -0.14 radian/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 25
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-32, Page No 217"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "#The symbols used here differ from the textbook solution to avoid conflict \n",
+      "t1=0 #s\n",
+      "t2=0.5 #s\n",
+      "t3=2.5 #s\n",
+      "t4=3**-1 #s\n",
+      "w=200 #rpm\n",
+      "w0=0 #rpm\n",
+      "\n",
+      "#Calculations\n",
+      "theta1=0.5*(w0+(w*60**-1))*t2 #rev\n",
+      "theta2=(w*60**-1)*(t3-t2) #rev\n",
+      "theta3=(2**-1)*((w*60**-1)+w0)*t4 #rev here the values of w and w0 are interchanged but essentially the value comes out to be the same hence the decleration has not been changed\n",
+      "theta=theta1+theta2+theta3 #rev\n",
+      "\n",
+      "#Result\n",
+      "print'The wheel undergoes',round(theta,2),\"revolutions\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The wheel undergoes 8.06 revolutions\n"
+       ]
+      }
+     ],
+     "prompt_number": 33
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-34, Page No 218"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=1 #s\n",
+      "r=4 #m\n",
+      "\n",
+      "#Calculations\n",
+      "s=t**3+3 #m\n",
+      "theta=s/r #rad\n",
+      "dtheta_dt=0.75*t**2 #rad/s\n",
+      "Vx=-4*sin(theta)*dtheta_dt #m/s\n",
+      "Vy=4*cos(theta)*dtheta_dt #m/s\n",
+      "V=(Vx**2+Vy**2)**0.5 #m/s\n",
+      "\n",
+      "#Result\n",
+      "print'The components of  velocity are:'\n",
+      "print'Vx=',round(Vx,2),\"m/s\"\n",
+      "print'Vy=',round(Vy,2),\"m/s\"\n",
+      "print'V=',round(V),\"m/s\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The components of  velocity are:\n",
+        "Vx= -2.52 m/s\n",
+        "Vy= 1.62 m/s\n",
+        "V= 3.0 m/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 35
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-35, Page No 218"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=1 #s\n",
+      "theta=1 #rad\n",
+      "\n",
+      "#Calculations\n",
+      "dtheta_dt=0.75*t**2 #rad/s\n",
+      "acc=1.5*t #rad/s**2\n",
+      "ax=-4*cos(theta)*dtheta_dt**2-(4*sin(theta)*acc) #m/s**2 (to left)\n",
+      "ay=-4*sin(theta)*dtheta_dt**2+(4*cos(theta)*acc) #m/s**2 (up)\n",
+      "a=sqrt(ax**2+ay**2) #m/s**2\n",
+      "\n",
+      "#result\n",
+      "print'The acceleration is',round(a,2),\"m/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The acceleration is 6.41 m/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 38
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-36, Page No 218"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=2 #s\n",
+      "\n",
+      "#Calculations\n",
+      "#Velocity\n",
+      "vx=8*t-3 #ft/s\n",
+      "vy=3*t**2 #ft/s\n",
+      "v=sqrt(vx**2+vy**2) #ft/s\n",
+      "theta_x=arctan(vy*vx**-1)*(180/pi) #degrees\n",
+      "#Acceleration\n",
+      "ax=8 #ft/s**2\n",
+      "ay=6*t #ft/s**2\n",
+      "a=sqrt(ax**2+ay**2) #ft/s**2\n",
+      "phi_x=arctan(ay*ax**-1)*(180/pi) #degrees\n",
+      "\n",
+      "#Result\n",
+      "print'The velocity is',round(v,1),\"ft/s\"\n",
+      "print'and the angle is',round(theta_x,1),\"degrees\"\n",
+      "print'The acceleration is',round(a,1),\"ft/s**2\"\n",
+      "print'and the angle it makes is',round(phi_x,1),\"degrees\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The velocity is 17.7 ft/s\n",
+        "and the angle is 42.7 degrees\n",
+        "The acceleration is 14.4 ft/s**2\n",
+        "and the angle it makes is 56.3 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 46
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-37, Page No 219"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "V_ao=29.3 #ft/s\n",
+      "OA=50 #ft\n",
+      "theta=45 #degrees\n",
+      "OB=50*sqrt(2) #ft\n",
+      "\n",
+      "#Calculations\n",
+      "w_ao=V_ao/OA #rad/s\n",
+      "V_bo=V_ao*cos(theta) #ft/s\n",
+      "w_bo=V_bo/OB #rad/s\n",
+      "\n",
+      "#Result\n",
+      "print'The angular velocity with respect to the observer is',round(w_ao,3),\"rad/s\"\n",
+      "print' The angular velocity after moving 50ft is',round(w_bo,3),\"rad/s\"\n",
+      "# The answer for w_bo is incorrect in textbook"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The angular velocity with respect to the observer is 0.586 rad/s\n",
+        " The angular velocity after moving 50ft is 0.218 rad/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 47
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-38, Page No 219"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initiliztaion of variables\n",
+      "# as theta=30 degrees\n",
+      "costheta=sqrt(3)*2**-1\n",
+      "tantheta=sqrt(3)**-1\n",
+      "r=[100*tantheta*(180/pi),100] #ft\n",
+      "v=17.6 #ft/s\n",
+      "\n",
+      "#Calculations\n",
+      "v_1=100*costheta**-1*costheta**-1\n",
+      "w=v/v_1 #rad/s (clockwise)\n",
+      "\n",
+      "#result\n",
+      "print'The angular velocity is',round(w,3),\"rad/s clockwise\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The angular velocity is 0.132 rad/s clockwise\n"
+       ]
+      }
+     ],
+     "prompt_number": 53
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-39, Page No 220"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "t=2 #s\n",
+      "\n",
+      "#Calculations\n",
+      "Vx=20*t+5 #m/s\n",
+      "Vy=t**2-20 #m/s\n",
+      "#As indefinite integral is not possible \n",
+      "x=10*t**2+5*t+5 #m\n",
+      "y=0.5*t**2-20*t-15 #m\n",
+      "ax=20 #m/s**2\n",
+      "ay=2*t #m/s**2\n",
+      "\n",
+      "#Result\n",
+      "print'The displacement components are x=',round(x),\"m\",'and y=',round(y),\"m.\"\n",
+      "print'The velocity components are: Vx=',round(Vx),\"m/s\",'and Vy=',round(Vy),\"m/s\"\n",
+      "print'The acceleration components are: ax=',round(ax),\"m/s**2\",'and ay=',round(ay),\"m/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The displacement components are x= 55.0 m and y= -53.0 m.\n",
+        "The velocity components are: Vx= 45.0 m/s and Vy= -16.0 m/s\n",
+        "The acceleration components are: ax= 20.0 m/s**2 and ay= 4.0 m/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 55
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-40, Page No 221"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "d=0.1 #m\n",
+      "v=20 #m/s\n",
+      "a_g=6 #m/s**2\n",
+      "d2=0.150 #m\n",
+      "\n",
+      "#Calculations\n",
+      "r=d/2 #m\n",
+      "w=v/r #rad/s\n",
+      "vb=d2*0.5*w #m/s\n",
+      "alpha=a_g/r #rad/s**2\n",
+      "a_t=d2*0.5*alpha #rad/s**2 tangential acceleration\n",
+      "a_n=d2*0.5*w*w #m/s**2 normal acceleration\n",
+      "a=sqrt(a_t**2+a_n**2) #m/s**2 linear acceleration\n",
+      "\n",
+      "#Result\n",
+      "print'The linear velocity is',round(vb),\"m/s\"\n",
+      "print'The acceleration is',round(a),\"m/s**2\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The linear velocity is 30.0 m/s\n",
+        "The acceleration is 12000.0 m/s**2\n"
+       ]
+      }
+     ],
+     "prompt_number": 57
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.12-41, Page No 221"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Initilization of variables\n",
+      "# as theta=40 degrees\n",
+      "sintheta=0.64\n",
+      "costheta=0.77\n",
+      "tantheta=0.83\n",
+      "x=100 #ft\n",
+      "ax=0 #ft/s**2\n",
+      "ay=-32.2 #ft/s**2\n",
+      "\n",
+      "#Calculations\n",
+      "#vox=vocos40....(1)\n",
+      "#voy=vox*t-1/2(32.2)t^2...(2)\n",
+      "#Simplyfying eq (1) and eq(2)\n",
+      "t_f=((x*tantheta)/(0.5*(-ay)))**0.5 #s time of flight\n",
+      "Vo=x/(costheta*t_f) #ft/s\n",
+      "#As the max height occurs at half wat through the flight\n",
+      "t=t_f/2 #s\n",
+      "ymax=Vo*sintheta*t+(0.5*ay*t*t) #ft the formula has positive sign as ay is defined negative\n",
+      "\n",
+      "#result\n",
+      "print'The max height the ball will reach is',round(ymax,1),\"ft\"\n",
+      "\n",
+      "# The ans in textbook is incorrect"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The max height the ball will reach is 20.8 ft\n"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
+\ No newline at end of file