Q14 / 214 · NTA Abhyas (NEET) 2020 · Physics · Oscillations

A particle of mass $m$ is acted upon by a force $F = t^{2} - k x$ . Initially, the particle is at rest at the origin. Then

Solution

a = \frac{t^{2}}{m} - \frac{k}{m} x

\frac{d a}{d t} = \frac{1}{2} 2 t - \frac{k}{m} . \frac{d x}{d t}

\frac{d^{2} a}{d t^{2}} = \frac{2}{m} - \frac{k}{m} a

\frac{d^{2} a}{d t^{2}} + \frac{k}{m} a - \frac{2}{m} = 0

This is second order differential equation for acceleration, hence

a

will be in simple harmonic.

Hence, the correct answer is option: 'C'.