period of mass-spring

Question

Time period of mass m on spring k is:

RankGuru · Accepted Answer

For a mass $m$ attached to an ideal spring of constant $k$, the restoring force is $F = -kx$. 
Equating it to $ma$:
$m \frac{d^2x}{dt^2} = -kx \implies \frac{d^2x}{dt^2} + \left(\frac{k}{m}\right)x = 0$
Comparing with the standard SHM equation $\frac{d^2x}{dt^2} + \omega^2 x = 0$, we find:
$\omega = \sqrt{\frac{k}{m}}$
The time period $T$ is given by $T = \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k}}$.

Rank Guru

period of mass-spring

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