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

The correct option is B $\frac{K{T}^{2}g}{4{\pi }^2}$

Time period of the suspended mass executing SHM $T=2\pi \sqrt{\frac{M}{K}}$

Squaring both sides, we get the value of mass suspended.

Mass $M=\frac{T^{2}K}{4{\pi }^2}$

Thus weight of mass suspended $W=Mg$

$⟹$ $W=\frac{K{T}^2}{4{\pi }^2}g$