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 ** of oscillation.
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,
