Question

Consider a pulley of moment of inertia I supporting a block of mass m, tied to an ideal spring of stiffness k.

The block is slightly pulled downward and released. Determine its period of oscillation. 

Answer 1

In equilibrium

mg = T . T = kx ₀

Also, ∴ mg = kx₀ ...(i)

Let the block be displaced downward by x and moving with velocity dx/dt. Then

Differentiating it and setting to zero,

Using (i) and (ii), we get

Comparing it with standard equation of SHM,