Which of the following relationships between the acceleration a and the displacement $x$ of a particle involve simple harmonic motion?(a) $a=-10 x$(b) $a=100 x^{3}$

Which of the following relationships between the acceleration a and the displacement $x$ of a particle involve simple harmonic motion?
(a) $a=-10 x$
(b) $a=100 x^{3}$

CBSE | Class 11 | NCERT | Oscillations | Physics

Which of the following relationships between the acceleration a and the displacement $x$ of a particle involve simple harmonic motion?
(a) $a=-10 x$
(b) $a=100 x^{3}$

The condition of SHM is stated below,

Acceleration is directly proportional to negative of displacement of particle.

If ‘ $\mathrm{a}$ ‘ is the acceleration,

$\mathrm{x}$ is the displacement

Then, for Simple Harmonic Motion,

$\mathrm{a}=-\mathrm{kx}$ where $\mathrm{k}$ is constant

(a) $a=-10 x$

This is in the form of $a=-k x$

Therefore, this is SHM

(b) $\mathrm{a}=100 \mathrm{x}^{3}$

It is clear it is not SHM