Question

A mass $m$ attached to free end of a spring executes SHM with a period of $1 \,s$ If the mass is increased by $3\, kg$ the period of oscillation increases by one second, the value of mass $m$ is ______$kg$

Answer 1

Correct Answer: 1

The correct answer is 1.
$T=2\pi \sqrt{\frac{m}{k}}=1$
$T^{\prime }=2\pi \sqrt{\frac{m+3}{k}}=2$
$\frac{T}{T^{\prime }}=\sqrt{\frac{m}{m+3}}=\frac{1}{2}$
$\Rightarrow \frac{m}{m+3}=\frac{1}{4}$
$m=1$