A solid cylinder of mass \( m \) is attached to a horizontal spring with force constant \( k \)....

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A solid cylinder of mass \( m \) is attached to a horizontal spring with force constant \( k \). The cylinder can roll without slipping along the horizontal plane. (See the accompanying figure.) Show that the centre of mass of the cylinder executes simple harmonic motion with a period \( T=2 \pi \sqrt{\frac{3 m}{2 k}} \), if displaced from mean position.
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