Question

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

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

Answer 1

Answer: (C)

executes simple harmonic motion

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