Question

A spring mass system is performing simple harmonic motion. Suddenly, a constant force $F$ is applied to the mass. Choose the correct statement. Assume that $F$ is lesser than the maximum spring force.

• A. Time period increases, the mean position remains the same.
• B. Time period decreases, the mean position remains the same.
• C. Time period remains the same, but the mean position gets shifted.
• D. Both time period and mean position get changed.

Answer 1

The correct option is C Time period remains the same, but the mean position gets shifted.

Time period of spring-block system
$T=2\pi \sqrt{\frac{m}{K}}$ doesn't depend on the net force on the block. Hence, time period remains the same.

Initially (without the force $F$, mean position is at $x=0$ [unstretched spring]
After $F$ is applied, applying force equation on block,
At mean position,
$F_{\text{net}}=F-K{x}_0=0$
$\Rightarrow x_0=\frac{F}{K}$
Hence, the mean position gets shifted.