Elastic behaviour of solids

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Question

A mass M attached to a spring oscillates with a period of 1s. If the mass is increased by 3 kg, the assuming that Hookes’ law is obeyed. The period increases by 1s. Find the value of M (in kg)

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Solution

$1 = 2 π \sqrt{\frac{M}{k}} a n d 2 = 2 π \sqrt{\frac{M + 3}{k}}$
Dividing these quations we get $4 = \frac{M + 3}{M} \Rightarrow M = 1 k g$

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