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. $\frac{KT^{2}g}{4\pi^{2}}$
• C. $\frac{KTg}{2\pi^{2}}$
• D. $\frac{KT^{2}g}{2\pi^{2}}$

Answer 1

Answer: (B)

Time period of oscillation of the block
$T =2 \pi \sqrt{\frac{m}{k}} \Rightarrow \frac{T^{2}}{4 \pi^{2}}=\frac{m}{k} $
or $m =\frac{T^{2} k}{4 \pi^{2}}$
Weight of the mass, $w=m g=\frac{k T^{2} g}{4 \pi^{2}}$