Rolling Cylinder on a Spring

MediumPhysElo Quiz #3

17.Rolling Cylinder on a Spring

+10

A uniform solid cylinder of mass

M

and radius

R

is placed on a horizontal surface, where it rolls without slipping. A massless string is wrapped around the circumference of the cylinder. The string exits horizontally from the top of the cylinder and connects to one end of an ideal spring of spring constant

k

. The other end of the spring is attached to a fixed vertical wall. The system is initially in equilibrium. If the cylinder is slightly displaced and released, what is the frequency

f

of the resulting oscillations?

\frac{1}{2\pi}\sqrt{\frac{2k}{3M}}

\frac{1}{2\pi}\sqrt{\frac{k}{M}}

\frac{1}{2\pi}\sqrt{\frac{4k}{3M}}

\frac{1}{2\pi}\sqrt{\frac{8k}{3M}}

\frac{1}{2\pi}\sqrt{\frac{4k}{M}}

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