A classical mechanics problem by Krishna Shankar

A solid cylinder of mass \(m=1 \text{ kg} \) is kept in equilibrium on a horizontal surface.

Two unstretched springs of forces \(k_1=10 \text{ Nm}^{-1}\) and \(k_2=20 \text{ Nm}^{-1}\) are attached to the cylinder as shown in figure.
Find the period (in seconds, \(s\)) of small oscillations.

Assume that the cylinder rolls without sliding.

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