Physics - SHM Question with Solution | TestHub

The time period of a mass suspended from a vertical spring is given by $T=2\pi \sqrt{\frac{m}{k}}$.

When the mass is at rest in equilibrium, the spring is stretched by a distance $x$ such that the restoring force balances the weight of the mass. Thus, $kx=mg$, which gives $\frac{m}{k}=\frac{x}{g}$.

Substituting this into the time period formula, we get $T=2\pi \sqrt{\frac{x}{g}}$.

Given $T=2$ s and $g={\pi }^2$, we have:

$2=2\pi \sqrt{\frac{x}{{\pi }^2}}$

$1=\pi \frac{\sqrt{x}}{\pi }$

$\sqrt{x}=1$

$x=1$ m.

Answer: $1$ m