Question

The equation o f motion o f particle is given by $\frac{dp}{dt}+m\omega^2y=0$ where p is momentum and y is its position. Then the particle

• A. moves along a circle
• B. moves along a parabola
• C. executes simple harmonic motion
• D. falls freely under gravity

Answer 1

Answer: (C)

$\frac{ dp }{ dt }+ m \omega^{2} y =0 $
$\frac{ dp }{ dt }=- m \omega^{2} y $
$\Rightarrow F =- m \omega^{2} y $
$\left(\therefore \frac{ dp }{ dt }=\text { force }\right)$
so, force is proportional to displacement so, it is simple harmonic motion