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 $..............kg$.
JEE MAIN 2023, Medium
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$T =2 \pi \sqrt{\frac{ m }{ k }}=1$
$T ^{\prime}=2 \pi \sqrt{\frac{ m +3}{ k }}=2$
$\frac{ T }{ T ^{\prime}}=\sqrt{\frac{ m }{ m +3}}=\frac{1}{2}$
$\Rightarrow \frac{ m }{ m +3}=\frac{1}{4}$
$m =1$
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