initial commit / add all books

32 files changed, 660 insertions, 0 deletions

diff --git a/3532/CH4/EX4.1/Ex4_1.sce b/3532/CH4/EX4.1/Ex4_1.sce
new file mode 100644
index 000000000..8dfd86913
--- /dev/null
+++ b/3532/CH4/EX4.1/Ex4_1.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.2.1\n')

+//given data

+//T=To*sin(W*t)

+To=0.588 //maximum value of periodic torque in N-m 

+W=4// freqency of applied force in rad/sec

+J=0.12//moment of inertia of wheel in kg-m^2

+Kt=1.176//stiffness of wire in N-m/rad

+Ct=0.392/1 //damping coefficient in N-m_sec/rad

+//calculations

+theta=To/sqrt((Kt-J*W^2)^2+(Ct*W)^2)//Equation for torsional vibration amplitude from Fig (4.2.2) and Eqn (4.2.5)

+MaxDcoup=Ct*W*theta//maximum damping couple in N-m

+if atan((Ct*W)/(Kt-J*W^2))>0  then

+    phiD=(180/%pi)*atan((Ct*W)/(Kt-J*W^2));//from eqn 4.2.6(in degrees)

+else

+    phiD=180+(180/%pi)*atan((Ct*W)/(Kt-J*W^2));

+    

+end

+//output

+mprintf(' a)The maximum angular displacement from rest position is %4.4f radians\n b)The maximum couple applied to dashpot is %4.4f N-m\n c)angle by which the angular displacement lags the torque is %4.4f degrees',theta,MaxDcoup,phiD)

diff --git a/3532/CH4/EX4.10.1/Ex4_12.sce b/3532/CH4/EX4.10.1/Ex4_12.sce
new file mode 100644
index 000000000..ccfe11d19
--- /dev/null
+++ b/3532/CH4/EX4.10.1/Ex4_12.sce
@@ -0,0 +1,28 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.1\n')

+//given data

+m=1000//mass of machine in kg

+Fo=490//amp of force in N

+f=180//freq inRPM

+//calculations

+//case a)

+K=1.96*10^6//total stiffness of springs in N/m

+Wn=sqrt(K/m)

+W=2*%pi*f/60

+bet=(W/Wn)

+zeta=0

+Xst1=Fo/K//amplitude of steady state

+X1=Xst1*(1/(sqrt((1-bet^2)^2+(2*zeta*bet)^2)))//amp of vibration Eqn 4.2.15 in Sec 4.2.1

+Ftr1=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+//case b)

+K=9.8*10^4//total stiffness of springs in N/m

+Wn=sqrt(K/m)

+W=2*%pi*f/60

+bet=(W/Wn)

+zeta=0

+Xst2=Fo/K//amplitude of steady state

+X2=Xst2*(1/(sqrt((1-bet^2)^2+(2*zeta*bet)^2)))//amp of vibration Eqn 4.2.15 in Sec 4.2.1

+Ftr2=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+//output

+mprintf(' a)The amplitude of motion of machine is %f m and the maximum force transmitted\n to the foundation because of the unbalanced force when\n K=1.96*10^6 N/m is %4.4f N\n b)for same case as in a)if K=9.8*10^4 N/m then\n the amplitude of motion of machine is %f m\n and the maximum force transmitted to the foundation because of\n the unbalanced force %4.4f N',X1,Ftr1,X2,Ftr2)

diff --git a/3532/CH4/EX4.10.2/Ex4_13.sce b/3532/CH4/EX4.10.2/Ex4_13.sce
new file mode 100644
index 000000000..4d2ebbd0e
--- /dev/null
+++ b/3532/CH4/EX4.10.2/Ex4_13.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.2\n')

+//given data

+m=75//mass of machine in kg

+K=11.76*10^5//stiffness of springs in N/m

+zeta=0.2

+mo=2//mass of piston in kg

+stroke=0.08//in m

+e=stroke/2//in m

+N=3000//spee in c.p.m

+//calculations

+Wn=sqrt(K/m)

+W=2*%pi*N/60

+bet=(W/Wn)

+y=(mo/m)

+Fo=mo*W^2*e//max force exerted

+X=y*e*bet^2/(sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn 4.3.2

+Ftr=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+mprintf(' a)The amplitude of vibration of machine is %f m and the \n the vibratory force Ftr transmitted to the foundation is %5.4f N',X,Ftr)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of values in textbook') 

diff --git a/3532/CH4/EX4.10.3/Ex4_14.sce b/3532/CH4/EX4.10.3/Ex4_14.sce
new file mode 100644
index 000000000..44a536569
--- /dev/null
+++ b/3532/CH4/EX4.10.3/Ex4_14.sce
@@ -0,0 +1,23 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.3\n')

+// given data

+m=20 //mass in kgs

+k=125600 //overall eqivalent stiffness i.e 4*31400 in N/m

+c=1568 //overall damping coefficient i.e 4*392 in N-sec/m

+n=500 //vibrating speed of machine in cpm

+//y=Ysin(w*t)

+Y=0.00005 //vibrating amplitude of machine in m

+W=2*%pi*n/60 //vibrating frequency in rad/sec

+Wn=sqrt(k/m) //natural frequency in rad/sec

+bet=(W/Wn) //speed ratio

+zeta=c/(2*sqrt(k*m)) //damping factor

+//calculations

+X=Y*sqrt((1+(2*zeta*bet)^2)/((1-bet^2)^2+(2*zeta*bet)^2)) //absolute amplitude of vibration of radio from eqn (4.4.6)

+Z=Y*((bet^2)/sqrt(((1-bet^2)^2+(2*zeta*bet)^2)))//from eqn 4.4.11

+FdynT=Z*sqrt((c*W)^2+k^2)//dynamic load total

+Fdyn=FdynT/4 //dynamic load on each isolator

+FdynTmax=m*W^2*X //max dynamic load on the isolators

+Fdynmax=FdynTmax/4 //max dynamic load on each isolator

+//output

+mprintf('a) The amplitude of vibration of radio is %f metres \n b)the dynamic load on each isolator due to vibration is %3.3f N',X,Fdyn)

diff --git a/3532/CH4/EX4.11.1/Ex4_15.sce b/3532/CH4/EX4.11.1/Ex4_15.sce
new file mode 100644
index 000000000..4696ee57f
--- /dev/null
+++ b/3532/CH4/EX4.11.1/Ex4_15.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.1\n')

+//given data

+T=2//period of free vibration in sec

+f=1//vertical harmonic frequency of machine in in Hz

+Z=2.5//amplitude of vibrotometer mass relative to vibrotometer frame in mm

+//calculations

+Wn=2*%pi/T

+W=2*%pi*f

+bet=(W/Wn)

+zeta=0//for vibrotometers

+Y=Z*(sqrt((1-bet^2)^2+(2*zeta*bet)^2))/bet^2//amplitude of vibration of machine Eqn 4.4.11 in Sec 4.4.2

+//output

+mprintf(' The amplitude of vibration of support of machine is %4.4f mm',Y)

diff --git a/3532/CH4/EX4.11.2/Ex4_16.sce b/3532/CH4/EX4.11.2/Ex4_16.sce
new file mode 100644
index 000000000..44826cf62
--- /dev/null
+++ b/3532/CH4/EX4.11.2/Ex4_16.sce
@@ -0,0 +1,35 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.2\n')

+//given data

+fn=5.75//natural frequency in Hz

+zeta=0.65

+ZbyY=1.01

+//case 1

+//substituting for (Z/Y)=1.01 and (W/Wn)=r^2 in Eqn 4.4.11 we get the quadratic eqn as follows

+//0.02*r^4-0.31*r^2+1=0

+//solving for r in above eqn whose rootes are r1 and r2

+r1=sqrt(((0.31)+sqrt(((-0.31)^2)-4*0.02*1))/(2*0.02))

+r2=sqrt(((0.31)-sqrt(((-0.31)^2)-4*0.02*1))/(2*0.02))

+if r1>r2 then

+    r=r1

+    else r=r2

+end

+bet=r//bet=(W/Wn)

+f1=bet*fn

+//case 2

+ZbyY=0.98

+//substituting for (Z/Y)=0.98 and (W/Wn)=r^2 in Eqn 4.4.11 we get the quadratic eqn as follows

+//0.04*r^4+0.31*r^2-1=0

+//solving for r in above eqn whose rootes are r3 and r4

+r3=sqrt((-0.31+sqrt(((0.31)^2)-4*0.04*-1))/(2*0.04))

+r4=sqrt((-0.31-sqrt(((0.31)^2)-4*0.04*-1))/(2*0.04))

+t1=real(r3)

+t2=real(r4)

+if t1>t2 then

+    r=r3

+    else r=r4

+end

+bet=r//bet=(W/Wn)

+f2=bet*fn

+mprintf('The lowest frequency beyond which the amplitude can be measured within\n  (i)one percent error is %4.4f Hz\n (ii)two percent error is %4.4f Hz',f1,f2)

diff --git a/3532/CH4/EX4.11.3/Ex4_17.sce b/3532/CH4/EX4.11.3/Ex4_17.sce
new file mode 100644
index 000000000..827e5825e
--- /dev/null
+++ b/3532/CH4/EX4.11.3/Ex4_17.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.3\n')

+//given data

+J=0.049//moment of inertia in kg-m^2

+Kt=0.98//stiffness in N-m/rad

+Ct=0.11//damping coefficient in N-m_sec/rad

+N=15//R.P.M

+thetaRD=2//relative amplitude between ring and shaft in degrees

+//calculations

+W=N*2*%pi/60 //frequency of  vibrating shaft in rad/sec

+Wn=sqrt(Kt/J) //natural freqency in rad/sec

+zeta=(Ct/(2*sqrt(Kt*J))) //damping factor

+thetaRR=(thetaRD/(57.3)) //relative amplitude in radians

+bet=(W/Wn)

+thetamax=thetaRR*((sqrt((1-bet^2)^2+(2*zeta*bet)^2)/bet^2))

+maxacc=(W^2)*thetamax

+//output

+mprintf('The maximum acceleration of the shaft is %4.4f rad/(sec^2)',maxacc)

diff --git a/3532/CH4/EX4.11.4/Ex4_18.sce b/3532/CH4/EX4.11.4/Ex4_18.sce
new file mode 100644
index 000000000..b568e3c24
--- /dev/null
+++ b/3532/CH4/EX4.11.4/Ex4_18.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.4\n')

+//given data

+RF=1800//resonant frequency in rpm

+L=0.050//lenght of steel reed in metres

+B=0.006//width of steel reed in metres

+t=0.00075//thickness of steel reed in metres

+E=19.6*10^10//young's modulus in N/(m^2)

+//calculations

+Wn=2*%pi*RF/60//natural frequency in radians

+I=(B*t^3)/12//moment of inertia in (m^4)

+m=3*E*I/((Wn^2)*L^3)//required mass

+//output

+mprintf('The required mass M to be placed at the end of the reeds of Frahm tachometer is %f Kgs',m)

diff --git a/3532/CH4/EX4.12/Ex4_12.sce b/3532/CH4/EX4.12/Ex4_12.sce
new file mode 100644
index 000000000..ccfe11d19
--- /dev/null
+++ b/3532/CH4/EX4.12/Ex4_12.sce
@@ -0,0 +1,28 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.1\n')

+//given data

+m=1000//mass of machine in kg

+Fo=490//amp of force in N

+f=180//freq inRPM

+//calculations

+//case a)

+K=1.96*10^6//total stiffness of springs in N/m

+Wn=sqrt(K/m)

+W=2*%pi*f/60

+bet=(W/Wn)

+zeta=0

+Xst1=Fo/K//amplitude of steady state

+X1=Xst1*(1/(sqrt((1-bet^2)^2+(2*zeta*bet)^2)))//amp of vibration Eqn 4.2.15 in Sec 4.2.1

+Ftr1=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+//case b)

+K=9.8*10^4//total stiffness of springs in N/m

+Wn=sqrt(K/m)

+W=2*%pi*f/60

+bet=(W/Wn)

+zeta=0

+Xst2=Fo/K//amplitude of steady state

+X2=Xst2*(1/(sqrt((1-bet^2)^2+(2*zeta*bet)^2)))//amp of vibration Eqn 4.2.15 in Sec 4.2.1

+Ftr2=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+//output

+mprintf(' a)The amplitude of motion of machine is %f m and the maximum force transmitted\n to the foundation because of the unbalanced force when\n K=1.96*10^6 N/m is %4.4f N\n b)for same case as in a)if K=9.8*10^4 N/m then\n the amplitude of motion of machine is %f m\n and the maximum force transmitted to the foundation because of\n the unbalanced force %4.4f N',X1,Ftr1,X2,Ftr2)

diff --git a/3532/CH4/EX4.13/Ex4_13.sce b/3532/CH4/EX4.13/Ex4_13.sce
new file mode 100644
index 000000000..4d2ebbd0e
--- /dev/null
+++ b/3532/CH4/EX4.13/Ex4_13.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.2\n')

+//given data

+m=75//mass of machine in kg

+K=11.76*10^5//stiffness of springs in N/m

+zeta=0.2

+mo=2//mass of piston in kg

+stroke=0.08//in m

+e=stroke/2//in m

+N=3000//spee in c.p.m

+//calculations

+Wn=sqrt(K/m)

+W=2*%pi*N/60

+bet=(W/Wn)

+y=(mo/m)

+Fo=mo*W^2*e//max force exerted

+X=y*e*bet^2/(sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn 4.3.2

+Ftr=Fo*sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//force transmitted,Eqn 4.10.2 in Sec 4.10.1

+mprintf(' a)The amplitude of vibration of machine is %f m and the \n the vibratory force Ftr transmitted to the foundation is %5.4f N',X,Ftr)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of values in textbook') 

diff --git a/3532/CH4/EX4.14/Ex4_14.sce b/3532/CH4/EX4.14/Ex4_14.sce
new file mode 100644
index 000000000..44a536569
--- /dev/null
+++ b/3532/CH4/EX4.14/Ex4_14.sce
@@ -0,0 +1,23 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.10.3\n')

+// given data

+m=20 //mass in kgs

+k=125600 //overall eqivalent stiffness i.e 4*31400 in N/m

+c=1568 //overall damping coefficient i.e 4*392 in N-sec/m

+n=500 //vibrating speed of machine in cpm

+//y=Ysin(w*t)

+Y=0.00005 //vibrating amplitude of machine in m

+W=2*%pi*n/60 //vibrating frequency in rad/sec

+Wn=sqrt(k/m) //natural frequency in rad/sec

+bet=(W/Wn) //speed ratio

+zeta=c/(2*sqrt(k*m)) //damping factor

+//calculations

+X=Y*sqrt((1+(2*zeta*bet)^2)/((1-bet^2)^2+(2*zeta*bet)^2)) //absolute amplitude of vibration of radio from eqn (4.4.6)

+Z=Y*((bet^2)/sqrt(((1-bet^2)^2+(2*zeta*bet)^2)))//from eqn 4.4.11

+FdynT=Z*sqrt((c*W)^2+k^2)//dynamic load total

+Fdyn=FdynT/4 //dynamic load on each isolator

+FdynTmax=m*W^2*X //max dynamic load on the isolators

+Fdynmax=FdynTmax/4 //max dynamic load on each isolator

+//output

+mprintf('a) The amplitude of vibration of radio is %f metres \n b)the dynamic load on each isolator due to vibration is %3.3f N',X,Fdyn)

diff --git a/3532/CH4/EX4.15/Ex4_15.sce b/3532/CH4/EX4.15/Ex4_15.sce
new file mode 100644
index 000000000..4696ee57f
--- /dev/null
+++ b/3532/CH4/EX4.15/Ex4_15.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.1\n')

+//given data

+T=2//period of free vibration in sec

+f=1//vertical harmonic frequency of machine in in Hz

+Z=2.5//amplitude of vibrotometer mass relative to vibrotometer frame in mm

+//calculations

+Wn=2*%pi/T

+W=2*%pi*f

+bet=(W/Wn)

+zeta=0//for vibrotometers

+Y=Z*(sqrt((1-bet^2)^2+(2*zeta*bet)^2))/bet^2//amplitude of vibration of machine Eqn 4.4.11 in Sec 4.4.2

+//output

+mprintf(' The amplitude of vibration of support of machine is %4.4f mm',Y)

diff --git a/3532/CH4/EX4.16/Ex4_16.sce b/3532/CH4/EX4.16/Ex4_16.sce
new file mode 100644
index 000000000..44826cf62
--- /dev/null
+++ b/3532/CH4/EX4.16/Ex4_16.sce
@@ -0,0 +1,35 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.2\n')

+//given data

+fn=5.75//natural frequency in Hz

+zeta=0.65

+ZbyY=1.01

+//case 1

+//substituting for (Z/Y)=1.01 and (W/Wn)=r^2 in Eqn 4.4.11 we get the quadratic eqn as follows

+//0.02*r^4-0.31*r^2+1=0

+//solving for r in above eqn whose rootes are r1 and r2

+r1=sqrt(((0.31)+sqrt(((-0.31)^2)-4*0.02*1))/(2*0.02))

+r2=sqrt(((0.31)-sqrt(((-0.31)^2)-4*0.02*1))/(2*0.02))

+if r1>r2 then

+    r=r1

+    else r=r2

+end

+bet=r//bet=(W/Wn)

+f1=bet*fn

+//case 2

+ZbyY=0.98

+//substituting for (Z/Y)=0.98 and (W/Wn)=r^2 in Eqn 4.4.11 we get the quadratic eqn as follows

+//0.04*r^4+0.31*r^2-1=0

+//solving for r in above eqn whose rootes are r3 and r4

+r3=sqrt((-0.31+sqrt(((0.31)^2)-4*0.04*-1))/(2*0.04))

+r4=sqrt((-0.31-sqrt(((0.31)^2)-4*0.04*-1))/(2*0.04))

+t1=real(r3)

+t2=real(r4)

+if t1>t2 then

+    r=r3

+    else r=r4

+end

+bet=r//bet=(W/Wn)

+f2=bet*fn

+mprintf('The lowest frequency beyond which the amplitude can be measured within\n  (i)one percent error is %4.4f Hz\n (ii)two percent error is %4.4f Hz',f1,f2)

diff --git a/3532/CH4/EX4.17/Ex4_17.sce b/3532/CH4/EX4.17/Ex4_17.sce
new file mode 100644
index 000000000..827e5825e
--- /dev/null
+++ b/3532/CH4/EX4.17/Ex4_17.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.3\n')

+//given data

+J=0.049//moment of inertia in kg-m^2

+Kt=0.98//stiffness in N-m/rad

+Ct=0.11//damping coefficient in N-m_sec/rad

+N=15//R.P.M

+thetaRD=2//relative amplitude between ring and shaft in degrees

+//calculations

+W=N*2*%pi/60 //frequency of  vibrating shaft in rad/sec

+Wn=sqrt(Kt/J) //natural freqency in rad/sec

+zeta=(Ct/(2*sqrt(Kt*J))) //damping factor

+thetaRR=(thetaRD/(57.3)) //relative amplitude in radians

+bet=(W/Wn)

+thetamax=thetaRR*((sqrt((1-bet^2)^2+(2*zeta*bet)^2)/bet^2))

+maxacc=(W^2)*thetamax

+//output

+mprintf('The maximum acceleration of the shaft is %4.4f rad/(sec^2)',maxacc)

diff --git a/3532/CH4/EX4.18/Ex4_18.sce b/3532/CH4/EX4.18/Ex4_18.sce
new file mode 100644
index 000000000..b568e3c24
--- /dev/null
+++ b/3532/CH4/EX4.18/Ex4_18.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.11.4\n')

+//given data

+RF=1800//resonant frequency in rpm

+L=0.050//lenght of steel reed in metres

+B=0.006//width of steel reed in metres

+t=0.00075//thickness of steel reed in metres

+E=19.6*10^10//young's modulus in N/(m^2)

+//calculations

+Wn=2*%pi*RF/60//natural frequency in radians

+I=(B*t^3)/12//moment of inertia in (m^4)

+m=3*E*I/((Wn^2)*L^3)//required mass

+//output

+mprintf('The required mass M to be placed at the end of the reeds of Frahm tachometer is %f Kgs',m)

diff --git a/3532/CH4/EX4.2.1/Ex4_1.sce b/3532/CH4/EX4.2.1/Ex4_1.sce
new file mode 100644
index 000000000..8dfd86913
--- /dev/null
+++ b/3532/CH4/EX4.2.1/Ex4_1.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.2.1\n')

+//given data

+//T=To*sin(W*t)

+To=0.588 //maximum value of periodic torque in N-m 

+W=4// freqency of applied force in rad/sec

+J=0.12//moment of inertia of wheel in kg-m^2

+Kt=1.176//stiffness of wire in N-m/rad

+Ct=0.392/1 //damping coefficient in N-m_sec/rad

+//calculations

+theta=To/sqrt((Kt-J*W^2)^2+(Ct*W)^2)//Equation for torsional vibration amplitude from Fig (4.2.2) and Eqn (4.2.5)

+MaxDcoup=Ct*W*theta//maximum damping couple in N-m

+if atan((Ct*W)/(Kt-J*W^2))>0  then

+    phiD=(180/%pi)*atan((Ct*W)/(Kt-J*W^2));//from eqn 4.2.6(in degrees)

+else

+    phiD=180+(180/%pi)*atan((Ct*W)/(Kt-J*W^2));

+    

+end

+//output

+mprintf(' a)The maximum angular displacement from rest position is %4.4f radians\n b)The maximum couple applied to dashpot is %4.4f N-m\n c)angle by which the angular displacement lags the torque is %4.4f degrees',theta,MaxDcoup,phiD)

diff --git a/3532/CH4/EX4.2.2/Ex4_2.sce b/3532/CH4/EX4.2.2/Ex4_2.sce
new file mode 100644
index 000000000..ebbfc6c90
--- /dev/null
+++ b/3532/CH4/EX4.2.2/Ex4_2.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.2.2\n')

+//given data

+Wd=9.8*2*%pi// damped natural freqency in rad/sec

+Wp=9.6*2*%pi//freqency from forced vibration test in rad/sec

+//calculations

+//(Wp/Wn)=sqrt(1-2*zeta^2)...(1) from Eqn 4.2.18 from Sec 4.2.1

+//(Wd/Wn)=sqrt(1-zeta^2)...(2) from Eqn 4.2.19 from Sec 4.2.1

+//dividing (1) by (2)

+x=(Wp/Wd)

+//x=[sqrt(1-2*zeta^2)]/[sqrt(1-zeta^2)]

+zeta=sqrt((1-x)/(2-x))//damping factor obtained on simplifying the above eqn

+//substituting for zeta in eqn 2 above

+Wn=Wd/sqrt(1-zeta^2)//natural frequency of system in rad/sec

+fn=Wn/(2*%pi)//natural frequency of system in Hz

+//output

+mprintf('The damping factor for the system is %f and\n the natural frequency is %4.4f rad/sec or %4.2f Hz',zeta,Wn,fn)

+mprintf('\nNOTE:The damping factor zeta given in textbook is 0.196,which is wrong.')

diff --git a/3532/CH4/EX4.2/Ex4_2.sce b/3532/CH4/EX4.2/Ex4_2.sce
new file mode 100644
index 000000000..ebbfc6c90
--- /dev/null
+++ b/3532/CH4/EX4.2/Ex4_2.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.2.2\n')

+//given data

+Wd=9.8*2*%pi// damped natural freqency in rad/sec

+Wp=9.6*2*%pi//freqency from forced vibration test in rad/sec

+//calculations

+//(Wp/Wn)=sqrt(1-2*zeta^2)...(1) from Eqn 4.2.18 from Sec 4.2.1

+//(Wd/Wn)=sqrt(1-zeta^2)...(2) from Eqn 4.2.19 from Sec 4.2.1

+//dividing (1) by (2)

+x=(Wp/Wd)

+//x=[sqrt(1-2*zeta^2)]/[sqrt(1-zeta^2)]

+zeta=sqrt((1-x)/(2-x))//damping factor obtained on simplifying the above eqn

+//substituting for zeta in eqn 2 above

+Wn=Wd/sqrt(1-zeta^2)//natural frequency of system in rad/sec

+fn=Wn/(2*%pi)//natural frequency of system in Hz

+//output

+mprintf('The damping factor for the system is %f and\n the natural frequency is %4.4f rad/sec or %4.2f Hz',zeta,Wn,fn)

+mprintf('\nNOTE:The damping factor zeta given in textbook is 0.196,which is wrong.')

diff --git a/3532/CH4/EX4.3.1/Ex4_3.sce b/3532/CH4/EX4.3.1/Ex4_3.sce
new file mode 100644
index 000000000..43d47e288
--- /dev/null
+++ b/3532/CH4/EX4.3.1/Ex4_3.sce
@@ -0,0 +1,20 @@
+clc

+clear

+mprintf('Mechanical vibrations b G.K.Grover\n Example 4.3.1\n')

+//given data

+m=1200//mass of motor in kg

+mo=1//unbalanced mass on motor in kg

+e=0.06//location of unbalanced mass from motor in m

+Wn=2210*(2*%pi/60)//resonant freq in rad/sec

+W=1440*(2*%pi/60)//operating freq 

+//calculations

+//case 1

+zeta=0.1

+bet=(W/Wn)

+y=(mo/m)//from eqn 4.3.2

+X1=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//case 2

+zeta=0

+X2=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//output

+mprintf('If the damping is less than 0.1 then the amplitude of \n vibration will be between %f m and %f m',X1,X2)

diff --git a/3532/CH4/EX4.3.2/Ex4_4.sce b/3532/CH4/EX4.3.2/Ex4_4.sce
new file mode 100644
index 000000000..d02fc736f
--- /dev/null
+++ b/3532/CH4/EX4.3.2/Ex4_4.sce
@@ -0,0 +1,22 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.3.2\n')

+//given data

+m=320//mass of engine in kg

+mo=24//reciprocating mass on motor in kg

+r=0.15//vertical stroke in m

+e=r/2

+delst=0.002//stati defln in m

+C=490/(0.3)//damping recistance in N-sec/m

+g=9.81// gravity in m/sec^2

+N=480//speed in rpm in case b)

+//calculation

+Wn=sqrt(g/delst) //natural freqency in rad/sec

+Nr=Wn/(2*%pi)*60 //resonant speed in rpm

+W=(2*%pi*N/60)

+bet=(W/Wn)

+zeta=(C/(2*m*Wn)) //damping factor

+y=(mo/m)//from eqn 4.3.2

+X=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//output

+mprintf(' a)speed of driving shaft at which esonance occurs is %4.4f RPM\n b)The amplitude of steady state forced vibrations when the driving shaft \n of the engine rotates at 480 RPM is %f m',Nr,X) 

diff --git a/3532/CH4/EX4.3/Ex4_3.sce b/3532/CH4/EX4.3/Ex4_3.sce
new file mode 100644
index 000000000..43d47e288
--- /dev/null
+++ b/3532/CH4/EX4.3/Ex4_3.sce
@@ -0,0 +1,20 @@
+clc

+clear

+mprintf('Mechanical vibrations b G.K.Grover\n Example 4.3.1\n')

+//given data

+m=1200//mass of motor in kg

+mo=1//unbalanced mass on motor in kg

+e=0.06//location of unbalanced mass from motor in m

+Wn=2210*(2*%pi/60)//resonant freq in rad/sec

+W=1440*(2*%pi/60)//operating freq 

+//calculations

+//case 1

+zeta=0.1

+bet=(W/Wn)

+y=(mo/m)//from eqn 4.3.2

+X1=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//case 2

+zeta=0

+X2=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//output

+mprintf('If the damping is less than 0.1 then the amplitude of \n vibration will be between %f m and %f m',X1,X2)

diff --git a/3532/CH4/EX4.4.1/Ex4_5.sce b/3532/CH4/EX4.4.1/Ex4_5.sce
new file mode 100644
index 000000000..6b19a1838
--- /dev/null
+++ b/3532/CH4/EX4.4.1/Ex4_5.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.1\n')

+//given data

+T=0.8//time period of free vibration in sec

+t=0.3//time for which the vertical distance has to be calculated

+//y=18*sin(2*pi*t)

+Y=18//max amplitude in mm

+//calculations

+W=2*%pi

+Wn=(2*%pi/T)

+bet=(W/Wn)

+x=(Y/(1-bet^2))*(sin(W*t)-bet*sin(Wn*t))// from eqn 4.4.17 explained in the same problem

+//output

+mprintf('The vertical distance moved by mass in the first 0.3 sec is %4.4f mm',x)

diff --git a/3532/CH4/EX4.4.2/Ex4_6.sce b/3532/CH4/EX4.4.2/Ex4_6.sce
new file mode 100644
index 000000000..9a40f5466
--- /dev/null
+++ b/3532/CH4/EX4.4.2/Ex4_6.sce
@@ -0,0 +1,20 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.2\n')

+//given data

+m=0.9//mass in kg

+K=1960//stiffness in N/m

+Y=5//amp of vibration of support in m

+N=1150//frequency in cycles per min

+//calculations

+Wn=sqrt(K/m)

+W=N*2*%pi/60//frequency of  vibration of support

+bet=(W/Wn)

+//case 1

+zeta=0

+X1=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//case 2

+zeta =0.2

+X2=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//output

+mprintf('The amplitude of vibration when damping factor=0 is %4.4f mm \n If damping factor=0.2,then amplitude of vibration is %4.4f mm',X1,X2)

diff --git a/3532/CH4/EX4.4.3/Ex4_7.sce b/3532/CH4/EX4.4.3/Ex4_7.sce
new file mode 100644
index 000000000..975af1a15
--- /dev/null
+++ b/3532/CH4/EX4.4.3/Ex4_7.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.3\n')

+//given data

+delst=0.1//steady state defln in m

+g=9.81//acceleration due to gravity

+Y=0.08//amp of vibration of automobile in m

+lambda=14//wavelenght of profile in m

+//calculations

+Wn=sqrt(g/delst)

+fn=Wn/(2*%pi)//frequency of vibration of automobile in Hz

+Vc=(3600/1000)*lambda*fn//critical speed in km/hr

+V=60 //speed in km/hr

+W=V*(1000/3600)*(2*%pi/lambda)

+bet=(W/Wn)

+zeta=0

+X=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//output

+mprintf(' The critical speed of automobile %4.4f km/hr\n The amplitude of vibration at 60 Km/Hr is %4.4f m',Vc,X)

diff --git a/3532/CH4/EX4.4/Ex4_4.sce b/3532/CH4/EX4.4/Ex4_4.sce
new file mode 100644
index 000000000..d02fc736f
--- /dev/null
+++ b/3532/CH4/EX4.4/Ex4_4.sce
@@ -0,0 +1,22 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.3.2\n')

+//given data

+m=320//mass of engine in kg

+mo=24//reciprocating mass on motor in kg

+r=0.15//vertical stroke in m

+e=r/2

+delst=0.002//stati defln in m

+C=490/(0.3)//damping recistance in N-sec/m

+g=9.81// gravity in m/sec^2

+N=480//speed in rpm in case b)

+//calculation

+Wn=sqrt(g/delst) //natural freqency in rad/sec

+Nr=Wn/(2*%pi)*60 //resonant speed in rpm

+W=(2*%pi*N/60)

+bet=(W/Wn)

+zeta=(C/(2*m*Wn)) //damping factor

+y=(mo/m)//from eqn 4.3.2

+X=(y*e)*(bet)^2/sqrt((1-bet^2)^2+(2*zeta*bet)^2)//from eqn 4.3.2

+//output

+mprintf(' a)speed of driving shaft at which esonance occurs is %4.4f RPM\n b)The amplitude of steady state forced vibrations when the driving shaft \n of the engine rotates at 480 RPM is %f m',Nr,X) 

diff --git a/3532/CH4/EX4.5.1/Ex4_8.sce b/3532/CH4/EX4.5.1/Ex4_8.sce
new file mode 100644
index 000000000..b7f52cdb5
--- /dev/null
+++ b/3532/CH4/EX4.5.1/Ex4_8.sce
@@ -0,0 +1,17 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.5.1\n')

+//given data

+X=0.015//amplitude of vibration of spring mass dashpot system in m

+f=100//frquency  of vibration of spring mass dashpot system in Hz

+zeta=0.05

+fnD=22//damped natural frequency in Hz

+m=0.5//mass in kg

+//calculations

+W=2*%pi*fnD

+c=2*m*W*zeta// from Eqn 3.3.6 and Eqn 3.3.7

+Epercycl=%pi*c*(2*%pi*f)*X^2//Eqn 4.5.1...energy dissipated per cycle

+Epersec=Epercycl*f//energy dissipated per sec 

+//output

+mprintf(' The power required to vibrate spring mass dashpot system with \n an amplitude of 1.5 cm and at frequency of 100 Hz is %4.4f Watts',Epersec)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of value of pi') 

diff --git a/3532/CH4/EX4.5/Ex4_5.sce b/3532/CH4/EX4.5/Ex4_5.sce
new file mode 100644
index 000000000..6b19a1838
--- /dev/null
+++ b/3532/CH4/EX4.5/Ex4_5.sce
@@ -0,0 +1,15 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.1\n')

+//given data

+T=0.8//time period of free vibration in sec

+t=0.3//time for which the vertical distance has to be calculated

+//y=18*sin(2*pi*t)

+Y=18//max amplitude in mm

+//calculations

+W=2*%pi

+Wn=(2*%pi/T)

+bet=(W/Wn)

+x=(Y/(1-bet^2))*(sin(W*t)-bet*sin(Wn*t))// from eqn 4.4.17 explained in the same problem

+//output

+mprintf('The vertical distance moved by mass in the first 0.3 sec is %4.4f mm',x)

diff --git a/3532/CH4/EX4.6.1/Ex4_9.sce b/3532/CH4/EX4.6.1/Ex4_9.sce
new file mode 100644
index 000000000..5e07c87c7
--- /dev/null
+++ b/3532/CH4/EX4.6.1/Ex4_9.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.6.1\n')

+//given data

+mprintf('NOTE:The mass given in textbook should be equal\n to 3.7 kgs and not 8.7 Kgs')

+m=3.7//mass in kg

+g=9.81// gravity 

+K=7550////stiffness of in N/m

+u=0.22//coefficient of friction

+Fo=19.6//amp of force in N

+f=5//frequency of force 

+//calculations

+F=u*m*g//frictional force

+W=2*%pi*f

+Wn=sqrt(K/m)

+bet=(W/Wn)

+X=(Fo/K)*sqrt(1-(4*F/(%pi*Fo))^2)/(1-bet^2)//Eqn 4.6.2 in Sec 4.6

+Ceq=4*F/(%pi*W*X)//equivalent viscous damping Eqn 4.6.1 in Sec 4.6

+//output

+mprintf('\nThe amplitude of vibration of mass is %f m\n The equivalent viscous damping is %f N-sec/m',X,Ceq)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of value of pi in the taxtbook') 

diff --git a/3532/CH4/EX4.6/Ex4_6.sce b/3532/CH4/EX4.6/Ex4_6.sce
new file mode 100644
index 000000000..9a40f5466
--- /dev/null
+++ b/3532/CH4/EX4.6/Ex4_6.sce
@@ -0,0 +1,20 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.2\n')

+//given data

+m=0.9//mass in kg

+K=1960//stiffness in N/m

+Y=5//amp of vibration of support in m

+N=1150//frequency in cycles per min

+//calculations

+Wn=sqrt(K/m)

+W=N*2*%pi/60//frequency of  vibration of support

+bet=(W/Wn)

+//case 1

+zeta=0

+X1=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//case 2

+zeta =0.2

+X2=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//output

+mprintf('The amplitude of vibration when damping factor=0 is %4.4f mm \n If damping factor=0.2,then amplitude of vibration is %4.4f mm',X1,X2)

diff --git a/3532/CH4/EX4.7/Ex4_7.sce b/3532/CH4/EX4.7/Ex4_7.sce
new file mode 100644
index 000000000..975af1a15
--- /dev/null
+++ b/3532/CH4/EX4.7/Ex4_7.sce
@@ -0,0 +1,19 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.4.3\n')

+//given data

+delst=0.1//steady state defln in m

+g=9.81//acceleration due to gravity

+Y=0.08//amp of vibration of automobile in m

+lambda=14//wavelenght of profile in m

+//calculations

+Wn=sqrt(g/delst)

+fn=Wn/(2*%pi)//frequency of vibration of automobile in Hz

+Vc=(3600/1000)*lambda*fn//critical speed in km/hr

+V=60 //speed in km/hr

+W=V*(1000/3600)*(2*%pi/lambda)

+bet=(W/Wn)

+zeta=0

+X=Y*(sqrt(1+(2*zeta*bet)^2)/sqrt((1-bet^2)^2+(2*zeta*bet)^2))//Eqn (4.4.6)

+//output

+mprintf(' The critical speed of automobile %4.4f km/hr\n The amplitude of vibration at 60 Km/Hr is %4.4f m',Vc,X)

diff --git a/3532/CH4/EX4.8/Ex4_8.sce b/3532/CH4/EX4.8/Ex4_8.sce
new file mode 100644
index 000000000..b7f52cdb5
--- /dev/null
+++ b/3532/CH4/EX4.8/Ex4_8.sce
@@ -0,0 +1,17 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.5.1\n')

+//given data

+X=0.015//amplitude of vibration of spring mass dashpot system in m

+f=100//frquency  of vibration of spring mass dashpot system in Hz

+zeta=0.05

+fnD=22//damped natural frequency in Hz

+m=0.5//mass in kg

+//calculations

+W=2*%pi*fnD

+c=2*m*W*zeta// from Eqn 3.3.6 and Eqn 3.3.7

+Epercycl=%pi*c*(2*%pi*f)*X^2//Eqn 4.5.1...energy dissipated per cycle

+Epersec=Epercycl*f//energy dissipated per sec 

+//output

+mprintf(' The power required to vibrate spring mass dashpot system with \n an amplitude of 1.5 cm and at frequency of 100 Hz is %4.4f Watts',Epersec)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of value of pi') 

diff --git a/3532/CH4/EX4.9/Ex4_9.sce b/3532/CH4/EX4.9/Ex4_9.sce
new file mode 100644
index 000000000..5e07c87c7
--- /dev/null
+++ b/3532/CH4/EX4.9/Ex4_9.sce
@@ -0,0 +1,21 @@
+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 4.6.1\n')

+//given data

+mprintf('NOTE:The mass given in textbook should be equal\n to 3.7 kgs and not 8.7 Kgs')

+m=3.7//mass in kg

+g=9.81// gravity 

+K=7550////stiffness of in N/m

+u=0.22//coefficient of friction

+Fo=19.6//amp of force in N

+f=5//frequency of force 

+//calculations

+F=u*m*g//frictional force

+W=2*%pi*f

+Wn=sqrt(K/m)

+bet=(W/Wn)

+X=(Fo/K)*sqrt(1-(4*F/(%pi*Fo))^2)/(1-bet^2)//Eqn 4.6.2 in Sec 4.6

+Ceq=4*F/(%pi*W*X)//equivalent viscous damping Eqn 4.6.1 in Sec 4.6

+//output

+mprintf('\nThe amplitude of vibration of mass is %f m\n The equivalent viscous damping is %f N-sec/m',X,Ceq)

+mprintf('\nNOTE: slight differnce in answer compared to textbook\n is due approximation of value of pi in the taxtbook')