Question

Variations of acceleration a of a particle executing SHM with displacement x is:

Answer 1

The differential equation for S.H.M is given by $\frac{d^{2}x}{d{t}^2}+\left(\frac{k}{m}\right)x=0$ where $\frac{d^{2}x}{d{t}^2}$=acceleration,x=displacement ,m=mass

and k=force constant.

Also $\frac{k}{m}={\omega }^2$ where $\omega$=angular frequency

Reducing the above values in the equation of S.H.M

$\frac{d^{2}x}{d{t}^2}+{\omega }^{2}x=0$

$\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$

The negative sign implies that the acceleration and displacement are opposite in direction.