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+//To find the ratio nd/n
+clc
+//given
+//damping torque is directly proposrtional to the angular velocity
+C=12*10^6//Modulus of rigidity
+l=3//ft
+d=1//in
+g=32.2//ft/s^2
+I=500//lb ft^2 ; moment of inertia
+J=%pi*d^4/32
+q=C*J/(l*12)
+n=(1/(2*%pi))*(q*g*12/(I*12^2))^(1/2)
+//part 2 
+b1=(q*g*12/(I*12^2))
+a1=(b1/10.15)^(1/2)//by reducing equation 15.28
+nd=(1/(2*%pi))*(b1-(a1/2)^2)^(1/2)
+A=nd/n
+printf("\nThe frequency of natural vibration = %.2f per sec\nThe frequency of damped vibration = %.2f per sec\nThe ratio nd/n = %.3f\n",n,nd,A)