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+//to find the frequencies of the free longitudinal, transverse and torsional vibrations
+clc
+//given
+W=.3*2240//lb
+l=36//in
+D=3//in
+k=15//in
+A=%pi*(D/2)^2
+E=30*10^6//youngs modulus
+C=12*10^6
+g=32.2//ft/s^2
+d=W*l/(A*E)
+Fl=187.8/(d)^(1/2)
+I=%pi*(d/2)^4
+d1=W*(l^3)*64/(3*E*%pi*(3^4))
+Ft=187.8/(d1)^(1/2)
+j=%pi*3^4/32
+q=C*j/l
+Ftor=(1/(2*%pi))*(q*g*12/(W*k^2))^(1/2)
+F1=Ftor*60
+printf("\na) Frequency of Longitudinal vibrations = %.f per min\nb) Frequency of the transverse vibrations = %.f per min\nc) Frequency of the torsional vibration = %.f per min",Fl,Ft,F1)