A mass $m$ attached to a spring oscillates with a period of $3\,s$. If the mass is increased by $1\,kg$ the period increases by $1\,s$. The initial mass $m$ is
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$\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=\sqrt{\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}}$
$\Rightarrow \frac{\mathrm{T}}{\mathrm{T}+1}=\sqrt{\frac{\mathrm{M}}{\mathrm{M}+1}}$
$\Rightarrow \frac{3}{4}=\sqrt{\frac{M}{M+1}}$
$\Rightarrow \frac{9}{16}=\frac{\mathrm{M}}{\mathrm{M}+1} \Rightarrow 9 \mathrm{M}+9=16 \mathrm{M}$
$\Rightarrow 7 \mathrm{M}=9 \Rightarrow \mathrm{M}=\frac{9}{7} \mathrm{Kg}$
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