Question

The equation o f motion o f particle is given by $\frac{dp}{dt}+m{\omega }^{2}y=0$ 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