Question

A mass is suspended from a spring having spring constant k is displaced vertically and released, it oscillates with period T. The weight of the mass suspended is _________. (g = gravitational acceleration)

• A. $\frac{kTg}{4{\pi }^2}$
• B. $\frac{k{T}^{2}g}{4{\pi }^2}$
• C. $\frac{kTg}{2{\pi }^2}$
• D. $\frac{k{T}^{2}g}{2{\pi }^2}$

Answer 1

Answer: (B)

$\frac{k{T}^{2}g}{4{\pi }^2}$

Time period of a spring-block system executing $SHM$ is $T=2\pi \sqrt{\frac{M}{k}}$

where, $M$ and $k$ is the mass of the block and spring constant respectively.

On squaring both sides and solving, we get $M=\frac{k{T}^2}{4{\pi }^2}$

$\therefore$ Weight of the mass suspended, $W=Mg=\frac{k{T}^{2}g}{4{\pi }^2}$