A cord is attached between a 0.5 kg block and a spring with a force constant K=20 N/m . The other end of the spring is attached to the wall and the cord is placed over a pulley (I= 0.60 MR^2) of mass 5 kg and radius 0.50 as shown in figure. (Assuming no slipping occurs). What is the frequency of the oscillations when the body is set in to motion.

A cord is attached between a 0.5 kg block and a spring with a force co

1.	A cord is attached between a 0.5 kg block and a spring with a force constant K=20 N/m . The other end of the spring is attached to the wall and the cord is placed over a pulley (I= 0.60 MR^2) of mass 5 kg and radius 0.50 as shown in figure. (Assuming no slipping occurs). What is the frequency of the oscillations when the body is set in to motion.
Answer» Solution :When block moves down by a small distance .x. from mean position. `E=-mg x + 1/2 K (x+x)^2 + 1/2 I omega^2` `(dE)/(dt) = 0 ` use mg= `kx_0` `V= R omega impliesomega = (vartheta)/(R)` `(DX)/(dt) = vartheta ,(dw)/(dt) = alpha , (dv)/(dt) =a,- mg vartheta + (kx + kx_0) vartheta + (IV)/(R) alpha = 0 ` Finally use a `= R alpha ` `-mg + kx + kx_0 + (I a)/(R^2) = 0 ` `(kx + (IA)/(R^2))=0 ` use `a = - omega^2 x`