When the cylinder is displaced towards right, (θ is angle of rotation of diameter of the cylinder about the contact point) then x1+2x2=Rθ x1+x1=Rθ x1=
Rθ
2
τ=−[kx1R+kRθR]
3
2
mR2α=−[
KR2θ
2
+KR2θ] α=−
k
m
θ;t1=π√
m
k
When cylinder moves towards left, then Torque about the contact point −kR2θ=