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}

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