A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period
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(b) As $mg$ produces extension $x$, hence $k = \frac{{mg}}{x}$
$T = 2\pi \sqrt {\frac{{(M + m)}}{k}} = 2\pi \sqrt {\frac{{(M + m)x}}{{mg}}} $
$T = 2\pi \sqrt {\frac{{(M + m)}}{k}} = 2\pi \sqrt {\frac{{(M + m)x}}{{mg}}} $
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