Two-mass pendulum

A simple pendulum of length \(\ell\) and bob mass \(m\) undergoes small oscillations with the standard period \(T = 2\pi\sqrt{\frac{\ell}g}.\)

We now attach the second string of length \(\ell\), with a bob of mass \(12m,\) and hang it from the first bob. If we give a small kick to the bob of mass \(m,\) initially the larger mass will hardly move while the small mass will oscillate with period \(T^\prime\).

Find \(\frac{T^\prime}T.\)

\(\)
Note: The ropes are massless and flexible.

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