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  4. The time period of a vibrating spring due to a mass m is T. For twice of its mass, the new time period will be:

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Q. The time period of a vibrating spring due to a mass $m$ is $T$. For twice of its mass, the new time period will be:

Rajasthan PMTRajasthan PMT 2004Oscillations

Solution:

The time period of spring
$T=2 \pi \sqrt{\left(\frac{m}{R}\right)} \,\,\,...(1)$
$k=$ force constant of spring
again $T'=2 \pi \sqrt{\left(\frac{m'}{k}\right)}$
$=2 \pi \sqrt{\left(\frac{2 m}{k}\right)} $
$\left(\because m'=2 m\right) \ldots(2)$
From equations (1) and (2)
$\therefore T'=\sqrt{2} T$