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  4. If a spring has time period T, and is cut into n equa parts, then the time period of each part will be

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Q. If a spring has time period $T$, and is cut into $n$ equa parts, then the time period of each part will be

Oscillations

Solution:

For a spring, $T=2 \pi \sqrt{\frac{m}{k}}$
For each piece, spring constant $=n k$
$\therefore T'=2 \pi \sqrt{\frac{m}{n k}}$
$ \therefore T'=2 \pi \sqrt{\frac{m}{k}} \times \frac{1}{\sqrt{n}}=\frac{T}{\sqrt{n}}$