Two solid cylinders connected with a short light rod about common axis have radius R and total mass M rest on a horizontal table top connected to a spring of spring constant k as shown. The cylinders are pulled to the left by x and released. There is sufficient friction for the cylinders to roll. Find time period of oscillation
Here, τ=Iα=−kx.R
or (MR22+MR2)α=−kxR
or
Rα=−2k3Mx
now,
a=Rα=−2k3Mx
thus, ω=√2k3M
Time period
T=2πω=2π√3M2k