Question

A body of mass m is suspended from a spring of force constant $K$. Its time period is $T$. If an additional mass $M$ is attached to $m$, then its time period becomes $4T$. The value of mass $M$ will be

Answer 1

Time period $T=2\pi \sqrt{\frac{m}{K}}$

New time period $T^{\prime }=4T=2\pi \sqrt{\frac{m+M}{K}}$

Or $4\times 2\pi \sqrt{\frac{m}{K}}=2\pi \sqrt{\frac{m+M}{K}}$

Or $16m=m+M$

$⟹M=15m$