JEE Advanced 2020 Full Test 4 Paper 2

A cylinder of mass m=3kg and radius R=2m is attached to a massless spring-pulley system as shown in the figure and all the springs are in their natural length at t=0. The friction is sufficient to cause pure rolling of the cylinder. What is the time period (in sec.) of cylinder for small horizontal displacement? (spring constant k=2N∕m and π=3.14)