Q. 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 $A\left( mm\ s^{- 2} \right)\ \ \ 16\ \ \ \ \ \ \ 8\ \ \ \ \ 0\ \ \ - 8\ \ - 16$ $x\ (mm)\ \ \ \ \ \ \ \ - 4\ \ - 2\ \ \ \ 0\ \ \ \ \ \ \ 2\ \ \ \ \ \ \ 4$ The period of the motion is
A) $\frac{1}{\pi}s$
B) $\frac{2}{\pi}s$
C) $\frac{\pi}{2}s$
D) $\pi\ s$
Explanation
(d) $|A| = \omega^{2}x \Rightarrow \frac{|A|}{x} = \omega^{2}$
From the given value $\frac{|A|}{x} = \omega^{2} = 4 \Rightarrow \omega = 2$
Also$\ \omega = \frac{2\pi}{T} \Rightarrow 2 = \frac{2\pi}{T} \Rightarrow T = \pi\ sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.