A pulley in the form of a circular disc of mass \(m\) and radius \(r\) has the groove cut all along the perimeter. A string whose one end is attached over to the ceiling passes over this disc pulley and its other end is attached to a spring of spring constant k. The other end of the spring is attached to the ceiling as shown in the figure. Find the time period of vertical oscillations of the centre of mass assuming that the string does not slip over the pulley?

This problem is a part of Tessellate S.T.E.M.S.

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## Comments

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TopNewest\[\omega ^2=\frac {4kx}{1+\frac {I_{cm}}{mR^2}}\],therefore here \(\omega =\sqrt \frac {8k}{3m}\)

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how u derived the first formula

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Refer HC Verma. The question had been directly copied from there

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2pi_/(3m/8k)

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π(m/k)^(1/2)

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