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+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