Write the formula for the time period (T) of | vedclass

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(A) For a particle of mass $m$ executing $SHM$ under a restoring force $F = -kx$,the equation of motion is $m \frac{d^2x}{dt^2} = -kx$.This can be rew

Vedclass · Accepted Answer

$T = 2\pi \sqrt{\frac{m}{k}}$

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(A) For a particle of mass $m$ executing $SHM$ under a restoring force $F = -kx$,the equation of motion is $m \frac{d^2x}{dt^2} = -kx$.This can be rewritten as $\frac{d^2x}{dt^2} + \frac{k}{m}x = 0$.Comparing this with the standard $SHM$ equation $\frac{d^2x}{dt^2} + \omega^2x = 0$,we get $\omega^2 = \frac{k}{m}$,which implies $\omega = \sqrt{\frac{k}{m}}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,we get $T = 2\pi \sqrt{\frac{m}{k}}$.

Write the formula for the time period $(T)$ of a particle executing Simple Harmonic Motion $(SHM)$.

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