The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
AIPMT 2010, Medium
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A mass $M$ is suspended from a massless spring of spring constant $k$ as shown in figure $(a)$. Then,
Time period of oscillation is
$T=2 \pi \sqrt{\frac{M}{k}}$
When a another mass $M$ is also suspended with it as shown in figure $(b).$
Then,
Time period of oscillation is
$T^{\prime} =2 \pi \sqrt{\frac{M+M}{k}}=2 \pi \sqrt{\frac{2 M}{k}}$
$=\sqrt{2}(2 \pi \sqrt{\frac{M}{k}})=\sqrt{2} T \quad(\text { Using }(\mathrm{i}))$
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