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+clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 2.5.2\n')
+//given data
+G=0.83*10^11//rigidity modulus in N/m^2
+J=14.7 //mass moment of inertia in kg-m^2
+l1=0.6 //lenght of section 1 in m
+l2=1.8 //lenght of section 2 in m
+l3=0.25 //lenght of section 3 in m
+d1=0.05 //dia of section 1 in m
+d2=0.08 //dia of section 2 in m
+d3=0.03 //dia of section 3 in m
+//calculations
+Kt1=(G/l1)*(%pi/32)*d1^4 //(%pi/32)*d^4 is the section modulus
+Kt2=(G/l2)*(%pi/32)*d2^4
+Kt3=(G/l3)*(%pi/32)*d3^4
+Kt=1/((1/Kt1)+(1/Kt2)+(1/Kt3)) //total effective stiffness of the torsional system
+Wn=sqrt(Kt/J)//natural freq in rad/sec
+fn=Wn/(2*%pi) //natural freq in Hz
+//output
+mprintf(' The natural frequency of torsional oscillation for the given system is\n %4.4f rad/sec or %4.4f Hz.',Wn,fn)
+mprintf('\nNOTE:Since the value of Kt in the textbook has been rounded of\n to 3 decimal places,the final answer varies slightly.')