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diff --git a/3594/CH15/EX15.9/Ex15_9.sce b/3594/CH15/EX15.9/Ex15_9.sce
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+//To find the  frequencies of the  free  torsional vibrations of the system
+clc
+//given
+Ia=2.5//ton ft^2
+Ib=7.5//ton ft^2
+Ic=3//ton ft^2
+g=32.2//ft/s^2
+AB=9.5//ft
+BC=25//ft
+d=8.5//in
+C=11.8*10^6//lb/in^2
+k=Ic/Ia//la/lc=k
+lc1=(25.6+(25.6^2-4*114.1)^(1/2))/2//from 1 and 2 , reducing using quadratic formula
+lc2=(25.6-(25.6^2-4*114.1)^(1/2))/2//from 1 and 2 , reducing using quadratic formula
+la1=lc1*k
+la2=lc2*k
+J=%pi*d^4/32
+q=C*J/(lc1*12)//torsional stiffness
+IC=Ic*2240*12^2/(g*12)//moment of inertia
+nc=(1/(2*%pi))*(q/IC)^(1/2)//fundamental frequency of vibration
+a1=nc*60
+a=floor(a1)
+n=16*(lc1/lc2)^(1/2)
+b=n*60
+printf("\nFundamental frequency of vibration = %.f per min\nTwo node frequency = %.f per min\n",a,b)