Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
(a) a=0.7 x
(b) \mathbf{a}=-\mathbf{2 0 0} \mathrm{x}^{2}
Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
(a) a=0.7 x
(b) \mathbf{a}=-\mathbf{2 0 0} \mathrm{x}^{2}

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=0.7 x

This is not in the form of a=-k x

So, it is not SHM

(b) a=-200 x^{2}

Clearly we can see, it is not SHM