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-rw-r--r--3532/CH3/EX3.2/Ex3_2.sce19
-rw-r--r--3532/CH3/EX3.3.2/Ex3_2.sce19
-rw-r--r--3532/CH3/EX3.3.3/Ex3_3.sce26
-rw-r--r--3532/CH3/EX3.4.1/Ex3_5.sce21
-rw-r--r--3532/CH3/EX3.5/Ex3_5.sce21
-rw-r--r--3532/CH3/EX3.6.1/Ex3_6.sce20
-rw-r--r--3532/CH3/EX3.6.2/Ex3_7.sce31
-rw-r--r--3532/CH3/EX3.6/Ex3_6.sce20
-rw-r--r--3532/CH3/EX3.7.1/Ex3_8.sce11
-rw-r--r--3532/CH3/EX3.7/Ex3_7.sce31
-rw-r--r--3532/CH3/EX3.8/Ex3_8.sce11
11 files changed, 230 insertions, 0 deletions
diff --git a/3532/CH3/EX3.2/Ex3_2.sce b/3532/CH3/EX3.2/Ex3_2.sce
new file mode 100644
index 000000000..b009c42d4
--- /dev/null
+++ b/3532/CH3/EX3.2/Ex3_2.sce
@@ -0,0 +1,19 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.3.2\n')
+//given data
+m=10 //mass of solid in Kg
+Kr=3000 //stiffness of natural rubber in N/m
+Kf=12000 //stiffness of felt in N/m
+Cr=100 //damping coefficient of natural rubber in N-sec/m
+Cf=330 //damping coefficient of felt in N-sec/m
+//calculations
+Ke=1/((1/Kf)+(1/Kr)) //equivalent stiffness in N/m
+Ce=1/((1/Cf)+(1/Cr)) //equivalent damping coefficient N-sec/m
+Wn=sqrt(Ke/m) // undamped natural freq in rad/sec
+fn=Wn/(2*%pi) // undamped natural freq in Hz
+zeta=Ce/(2*sqrt(Ke*m)) //damping factor
+Wd=sqrt(1-zeta^2)*Wn //damped natural freuency in rad/sec(eqn 3.3.16)
+fd=Wd/(2*%pi) // damped natural frequency in Hz
+//output
+mprintf(' The undamped natural frequency is %4.4f rad/sec or %4.4f Hz\n The damped natural freuency is %4.4f rad/sec or %4.4f Hz',Wn,fn,Wd,fd)
diff --git a/3532/CH3/EX3.3.2/Ex3_2.sce b/3532/CH3/EX3.3.2/Ex3_2.sce
new file mode 100644
index 000000000..b009c42d4
--- /dev/null
+++ b/3532/CH3/EX3.3.2/Ex3_2.sce
@@ -0,0 +1,19 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.3.2\n')
+//given data
+m=10 //mass of solid in Kg
+Kr=3000 //stiffness of natural rubber in N/m
+Kf=12000 //stiffness of felt in N/m
+Cr=100 //damping coefficient of natural rubber in N-sec/m
+Cf=330 //damping coefficient of felt in N-sec/m
+//calculations
+Ke=1/((1/Kf)+(1/Kr)) //equivalent stiffness in N/m
+Ce=1/((1/Cf)+(1/Cr)) //equivalent damping coefficient N-sec/m
+Wn=sqrt(Ke/m) // undamped natural freq in rad/sec
+fn=Wn/(2*%pi) // undamped natural freq in Hz
+zeta=Ce/(2*sqrt(Ke*m)) //damping factor
+Wd=sqrt(1-zeta^2)*Wn //damped natural freuency in rad/sec(eqn 3.3.16)
+fd=Wd/(2*%pi) // damped natural frequency in Hz
+//output
+mprintf(' The undamped natural frequency is %4.4f rad/sec or %4.4f Hz\n The damped natural freuency is %4.4f rad/sec or %4.4f Hz',Wn,fn,Wd,fd)
diff --git a/3532/CH3/EX3.3.3/Ex3_3.sce b/3532/CH3/EX3.3.3/Ex3_3.sce
new file mode 100644
index 000000000..0c30824a7
--- /dev/null
+++ b/3532/CH3/EX3.3.3/Ex3_3.sce
@@ -0,0 +1,26 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.3.3\n')
+//given data
+m=600//mass of gun barrel in Kgs
+k=294000//stiffness in N/m
+x=1.3//recoil of gun in meters
+//calculations
+E=0.5*k*x^2//energy stored at the end of recoil
+Vo=sqrt(2*E/m)//velocity of recoil
+Cc=2*sqrt(k*m)//critical damping in N-sec/m
+Wn=sqrt(k/m)//natural frequency of undamped vibration in rad/sec
+T=2*%pi/Wn//time period of undamped vibration in sec
+Trecoil=(1/4)*T//time period for recoil or outward stroke in sec
+//x=(1.3+28.8*t)*e^(-22.1*t) from eqn 3.3.24
+mprintf('a)the initial recoil velocity of barrel is %f m/s\nb)critical damping co-efficient of the dashpot which is engaged at\nthe end of recoil stroke is %f N-sec/m\n\nsubstituting the value for t in eqn 3.3.24,starting from t=0.1 sec\nwith an increment of 0.01sec we get the following observations\n',Vo,Cc)
+t=0.1
+for i=1:20
+ x=(1.3 +28.8*t)*exp(-22.1*t)
+ mprintf('x=%f at t=%f\n',x,t)
+ t=t+0.01
+end
+mprintf('As x approaches the value of 0.05m,the value of t=0.22sec')
+Trec=0.22
+Tret=Trecoil+Trec
+mprintf('\nc)Therefore time required for barrel to return to position 5cm from\n the initial position is %f sec',Tret)
diff --git a/3532/CH3/EX3.4.1/Ex3_5.sce b/3532/CH3/EX3.4.1/Ex3_5.sce
new file mode 100644
index 000000000..f5f515bd1
--- /dev/null
+++ b/3532/CH3/EX3.4.1/Ex3_5.sce
@@ -0,0 +1,21 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.4.1\n')
+//given data
+J=0.06 //moment of inertia of disc of pendulum in Kg-m^2
+G=4.4*10^10 //rigidity modulus in N/m^2
+l=0.4 //lenght of shaft in m
+d=0.1 //diametre of shaft in m
+a1=9 //amplitude of first oscillation in degrees
+a2=6 //amplitude of second oscillation in degrees
+a3=4 //amplitude of third oscillation in degrees
+//calculations
+delta=log(a1/a2) //logarithmic decrement eqn 3.4.1 explained in sec 3.4
+zeta=delta/sqrt(4*%pi^2+delta^2) //representing zeta from eqn 3.4.1 in sec 3.4
+Kt=(G/l)*(%pi/32)*d^4 //(%pi/32)*d^4 is the section modulus
+C=zeta*2*sqrt(Kt*J) // torsional damping coefficient which is the damping torque at unit velocity (similar to eqn 3.3.6 in sec 3.3)
+Wn=sqrt(Kt/J) // undamped natural freq in rad/sec
+T=2*%pi/(sqrt(1-zeta^2)*Wn) //periodic time of vibration
+fn=Wn/(2*%pi) //natural freq of undamped vibration
+//output
+mprintf(' a)logarithmic decrement is %4.4f\n b)damping torque at unit velocity is %4.4f N-m/rad\n c)periodic time of vibration is %4.5f sec\n frequency of vibration if the disc is removed from viscous fluid is %4.4f Hz',delta,C,T,fn)
diff --git a/3532/CH3/EX3.5/Ex3_5.sce b/3532/CH3/EX3.5/Ex3_5.sce
new file mode 100644
index 000000000..f5f515bd1
--- /dev/null
+++ b/3532/CH3/EX3.5/Ex3_5.sce
@@ -0,0 +1,21 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.4.1\n')
+//given data
+J=0.06 //moment of inertia of disc of pendulum in Kg-m^2
+G=4.4*10^10 //rigidity modulus in N/m^2
+l=0.4 //lenght of shaft in m
+d=0.1 //diametre of shaft in m
+a1=9 //amplitude of first oscillation in degrees
+a2=6 //amplitude of second oscillation in degrees
+a3=4 //amplitude of third oscillation in degrees
+//calculations
+delta=log(a1/a2) //logarithmic decrement eqn 3.4.1 explained in sec 3.4
+zeta=delta/sqrt(4*%pi^2+delta^2) //representing zeta from eqn 3.4.1 in sec 3.4
+Kt=(G/l)*(%pi/32)*d^4 //(%pi/32)*d^4 is the section modulus
+C=zeta*2*sqrt(Kt*J) // torsional damping coefficient which is the damping torque at unit velocity (similar to eqn 3.3.6 in sec 3.3)
+Wn=sqrt(Kt/J) // undamped natural freq in rad/sec
+T=2*%pi/(sqrt(1-zeta^2)*Wn) //periodic time of vibration
+fn=Wn/(2*%pi) //natural freq of undamped vibration
+//output
+mprintf(' a)logarithmic decrement is %4.4f\n b)damping torque at unit velocity is %4.4f N-m/rad\n c)periodic time of vibration is %4.5f sec\n frequency of vibration if the disc is removed from viscous fluid is %4.4f Hz',delta,C,T,fn)
diff --git a/3532/CH3/EX3.6.1/Ex3_6.sce b/3532/CH3/EX3.6.1/Ex3_6.sce
new file mode 100644
index 000000000..9fedb6e9c
--- /dev/null
+++ b/3532/CH3/EX3.6.1/Ex3_6.sce
@@ -0,0 +1,20 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.6.1\n')
+//given data
+m=5 //mass in spring mass system )in kg)
+k=980//stiffnes of spring in N/m
+u=0.025//coefficient of friction
+g=9.81//acceleration due to gravity
+//calculations
+F=u*m*g//frictional force in N
+Wn=sqrt(k/m)// freq of free oscillations in rad/sec
+fn=Wn/(2*%pi)// freq of free oscillations in Hz
+Ai=0.05//initial amplitude in m
+Ar=0.5*Ai//reduced amplitude in m
+totAreduc=Ai-Ar//total reduction in amp in m
+Areducpercycl=4*F/k //reduction in amplitude/cycle explained in section 3.6.2 in eqn 3.6.6
+n=round(totAreduc/Areducpercycl) //number of cycles for 50% reduction in amplitude
+Treduc=n*(2*%pi/Wn)//time taken to achieve 50%reduction
+//output
+mprintf(' a)The frequency of free oscillations is %4.4f rad/sec or %4.4f Hz\n b)number of cycles taken for 50 percent reduction in amplitude is %1.0f cycles\n c)time taken to achieve 50 percent reduction in amplitude is %4.4f sec',Wn,fn,n,Treduc)
diff --git a/3532/CH3/EX3.6.2/Ex3_7.sce b/3532/CH3/EX3.6.2/Ex3_7.sce
new file mode 100644
index 000000000..4d3b71f4a
--- /dev/null
+++ b/3532/CH3/EX3.6.2/Ex3_7.sce
@@ -0,0 +1,31 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.6.2\n')
+//given data
+k=9800//stiffnes of spring in N/m
+m=40 //mass in spring mass system )in kg)
+g=9.81//acceleration due to gravity
+F=49//frictional force in N
+x=0.126//total extension of spring in m
+xeq=m*g/k//extension of spring at equillibrium in m
+xi=x-xeq//initial extension of spring from equillibrium in m
+Alosspercycl=4*F/k//reduction in amplitude/cycle explained in section 3.6.2 in eqn 3.6.6
+n=int(xi/Alosspercycl)//number of complete cycles that system undergoes
+Af=xi-n*Alosspercycl//amplitude at the end of n cycles
+SF=k*Af//spring force acting on the upward direction for an extension of Af
+if F<SF then
+ disp('The spring will move up since spring force is greater than frictional force')
+ Xa=Af//assigning Af to a new variable Xa
+ Xb=0//assume Xb=0 at first
+ //solving the quadratic equation in Xb whose roots are Xb1 and Xb2
+ Xb1=(F+sqrt((-F)^2-(4*(0.5*k)*((-(1/2)*k*Xa^2)+F*Xa))))/k
+ Xb2=(F-sqrt((-F)^2-(4*(0.5*k)*((-(1/2)*k*Xa^2)+F*Xa))))/k
+ if int(Xb1-Xa)==0 then
+ Xb=Xb2
+ else
+ Xb=Xb1
+ end
+ finalext=xeq+Xb
+ mprintf(' The final extention of spring is %f m',finalext)
+ else disp('The spring will not move up since spring force is not greater than frictional force')
+end
diff --git a/3532/CH3/EX3.6/Ex3_6.sce b/3532/CH3/EX3.6/Ex3_6.sce
new file mode 100644
index 000000000..9fedb6e9c
--- /dev/null
+++ b/3532/CH3/EX3.6/Ex3_6.sce
@@ -0,0 +1,20 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.6.1\n')
+//given data
+m=5 //mass in spring mass system )in kg)
+k=980//stiffnes of spring in N/m
+u=0.025//coefficient of friction
+g=9.81//acceleration due to gravity
+//calculations
+F=u*m*g//frictional force in N
+Wn=sqrt(k/m)// freq of free oscillations in rad/sec
+fn=Wn/(2*%pi)// freq of free oscillations in Hz
+Ai=0.05//initial amplitude in m
+Ar=0.5*Ai//reduced amplitude in m
+totAreduc=Ai-Ar//total reduction in amp in m
+Areducpercycl=4*F/k //reduction in amplitude/cycle explained in section 3.6.2 in eqn 3.6.6
+n=round(totAreduc/Areducpercycl) //number of cycles for 50% reduction in amplitude
+Treduc=n*(2*%pi/Wn)//time taken to achieve 50%reduction
+//output
+mprintf(' a)The frequency of free oscillations is %4.4f rad/sec or %4.4f Hz\n b)number of cycles taken for 50 percent reduction in amplitude is %1.0f cycles\n c)time taken to achieve 50 percent reduction in amplitude is %4.4f sec',Wn,fn,n,Treduc)
diff --git a/3532/CH3/EX3.7.1/Ex3_8.sce b/3532/CH3/EX3.7.1/Ex3_8.sce
new file mode 100644
index 000000000..55624fded
--- /dev/null
+++ b/3532/CH3/EX3.7.1/Ex3_8.sce
@@ -0,0 +1,11 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.7.1\n')
+//given data
+fnA=12 //frequency of free vibrations of system A in Hz
+fnB=15 //frequency of free vibrations of system B in Hz
+TdA=4.5 //time taken by system A to damp out completely in sec
+//calculations
+TdB=fnA*TdA/fnB //time taken by system B to damp out completely in sec
+//output
+mprintf(' The time taken by system B to damp out completely is %4.4f sec',TdB)
diff --git a/3532/CH3/EX3.7/Ex3_7.sce b/3532/CH3/EX3.7/Ex3_7.sce
new file mode 100644
index 000000000..4d3b71f4a
--- /dev/null
+++ b/3532/CH3/EX3.7/Ex3_7.sce
@@ -0,0 +1,31 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.6.2\n')
+//given data
+k=9800//stiffnes of spring in N/m
+m=40 //mass in spring mass system )in kg)
+g=9.81//acceleration due to gravity
+F=49//frictional force in N
+x=0.126//total extension of spring in m
+xeq=m*g/k//extension of spring at equillibrium in m
+xi=x-xeq//initial extension of spring from equillibrium in m
+Alosspercycl=4*F/k//reduction in amplitude/cycle explained in section 3.6.2 in eqn 3.6.6
+n=int(xi/Alosspercycl)//number of complete cycles that system undergoes
+Af=xi-n*Alosspercycl//amplitude at the end of n cycles
+SF=k*Af//spring force acting on the upward direction for an extension of Af
+if F<SF then
+ disp('The spring will move up since spring force is greater than frictional force')
+ Xa=Af//assigning Af to a new variable Xa
+ Xb=0//assume Xb=0 at first
+ //solving the quadratic equation in Xb whose roots are Xb1 and Xb2
+ Xb1=(F+sqrt((-F)^2-(4*(0.5*k)*((-(1/2)*k*Xa^2)+F*Xa))))/k
+ Xb2=(F-sqrt((-F)^2-(4*(0.5*k)*((-(1/2)*k*Xa^2)+F*Xa))))/k
+ if int(Xb1-Xa)==0 then
+ Xb=Xb2
+ else
+ Xb=Xb1
+ end
+ finalext=xeq+Xb
+ mprintf(' The final extention of spring is %f m',finalext)
+ else disp('The spring will not move up since spring force is not greater than frictional force')
+end
diff --git a/3532/CH3/EX3.8/Ex3_8.sce b/3532/CH3/EX3.8/Ex3_8.sce
new file mode 100644
index 000000000..55624fded
--- /dev/null
+++ b/3532/CH3/EX3.8/Ex3_8.sce
@@ -0,0 +1,11 @@
+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 3.7.1\n')
+//given data
+fnA=12 //frequency of free vibrations of system A in Hz
+fnB=15 //frequency of free vibrations of system B in Hz
+TdA=4.5 //time taken by system A to damp out completely in sec
+//calculations
+TdB=fnA*TdA/fnB //time taken by system B to damp out completely in sec
+//output
+mprintf(' The time taken by system B to damp out completely is %4.4f sec',TdB)
generated by cgit (git 2.34.1) at 2025-03-08 08:00:14 +0000