Two-mass pendulum

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

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

Find TT.\frac{T^\prime}T.


Note: The ropes are massless and flexible.

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