# The pulley shown in the figure has a moment of inertia I about its axis and mass m. Find the time period of vertical oscillation of its center of mass. The spring has spring constant K and the string does not slip on the pulley?

##### 1 Answer

Mar 20, 2018

#### Answer:

See below.

#### Explanation:

Assuming the pulley of uniform material.

Pulley dynamics

then solving

we obtain

but

now considering the homogeneous differential equation

obtaining

period