Question

What is the relation between restoring force $\left(F\right)$ and displacement $\left(x\right)$ of a particle to perform SHM.

• A. $F\propto x^2$
• B. $F\propto x^{-2}$
• C. $F\propto x^{1/2}$
• D. $F\propto x$

Answer 1

Answer: (D)

$F\propto x$

Any SHM can be represented by a sinusoidal displacement motion.

Let displacement be given by, $x=A\sin (\omega t+\varphi )$

Thus, velocity is $v=\frac{dx}{dt}=A\omega \cos (\omega t+\varphi )$

Similarly, acceleration is given by, $a=\frac{dv}{dt}=-A{\omega }^2\sin (\omega t+\varphi )=-{\omega }^{2}x$

Thus, for SHM, $a=-{\omega }^{2}x$

Net restoring force is $F=-ma=m{\omega }^{2}x$

Thus, $F\propto x$