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(B) When an additional mass $m$ is added,the spring extends by a distance $x$. According to Hooke's Law,the restoring force is equal to the weight of

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$T = 2\pi \sqrt {\left( {\frac{{\left( {M + m} \right)x}}{{mg}}} \right)} $

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(B) When an additional mass $m$ is added,the spring extends by a distance $x$. According to Hooke's Law,the restoring force is equal to the weight of the added mass:$mg = Kx$where $K$ is the spring constant.From this,we can find the spring constant:$K = \frac{mg}{x}$Now,the total mass oscillating on the spring is $(M + m)$. The time period $T$ of a mass-spring system is given by the formula:$T = 2\pi \sqrt{\frac{	ext{Total Mass}}{K}}$Substituting the values of total mass and $K$:$T = 2\pi \sqrt{\frac{(M + m)}{\frac{mg}{x}}}$$T = 2\pi \sqrt{\frac{(M + m)x}{mg}}$

$A$ 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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