The period of oscillation of a mass M suspend | vedclass

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(D) The period of oscillation for a mass-spring system is given by the formula $T = 2\pi \sqrt{\frac{m}{k}}$,where $m$ is the mass and $k$ is the spri

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$\sqrt{2}T$

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(D) The period of oscillation for a mass-spring system is given by the formula $T = 2\pi \sqrt{\frac{m}{k}}$,where $m$ is the mass and $k$ is the spring constant.Initially,the mass is $M$,so $T = 2\pi \sqrt{\frac{M}{k}}$.When another mass $M$ is added,the total mass becomes $M' = M + M = 2M$.The new period of oscillation $T'$ will be $T' = 2\pi \sqrt{\frac{2M}{k}}$.Dividing the new period by the initial period: $\frac{T'}{T} = \frac{2\pi \sqrt{\frac{2M}{k}}}{2\pi \sqrt{\frac{M}{k}}} = \sqrt{\frac{2M}{M}} = \sqrt{2}$.Therefore,the new period is $T' = \sqrt{2}T$.

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

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