Question

A spring block system (mass = $m$, spring constant $k$) is placed on a smooth inclined plane ($\theta$= angle of inclination). The plane is accelerated horizontally with a such that the block does not loose contact with the plane. The time period of small oscillation of the block is

• A. $2\pi \sqrt{\frac{m}{k}}$
• B. $2\pi \sqrt{\frac{msin\theta }{k}}$
• C. $2\pi \sqrt{\frac{mg}{ka}}$
• D. none of the above

Answer 1

The correct option is A $2\pi \sqrt{\frac{m}{k}}$

if $x_0$ is elongation in equilibrium,
$\therefore ma\cos \theta +mg\sin \theta =k{x}_0$
For $x$ = elongation from equilibrium

net force $F=mg\sin \theta +ma\cos \theta -k(x_0+x)$
$=-kx$
$\therefore T=2\pi \sqrt{\frac{m}{k}}$