Values of the acceleration $A$ of a particle moving in simple harmonic motion as a function of its displacement $x$ are given in the table below. The period of the motion is
| $A (mm \,\,s^{-2}$) |
$16$ |
$8$ |
$0$ |
$- 8$ |
$- 16$ |
|
$x\;(mm)$ |
$- 4$ |
$- 2$ |
$0$ |
$2$ |
$4$ |
Medium
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(d) $|A| = \omega^2x$ ==> $\frac{{|A|}}{x} = {\omega ^2}$
From the given value $\frac{{|A|}}{x} = {\omega ^2} = 4$ ==> $\omega = 2.$
Also $\omega = \frac{{2\pi }}{T} \Rightarrow 2 = \frac{{2\pi }}{T}\, \Rightarrow T = \pi \,sec$
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