Question

A mass $M$ is suspended from a light spring. An additional mass $m$ added, displaces the spring further by a distance $X$ . Now, the combined mass will oscillate on the spring with time period

• A. $T=2\pi \sqrt{\frac{mg}{(M+m)X}}$
• B. $T=2\pi \sqrt{\frac{(M+m)X}{mg}}$
• C. $T=\frac{\pi }{2}\sqrt{\frac{mg}{(M+m)X}}$
• D. $T=2\pi \sqrt{\frac{(M+m)}{mgX}}$

Answer 1

Answer: (B)

As an additional mass $m$ is added, the spring is further stretched by a distance $X$ , therefore
$kX=mg$
$\Rightarrow k=\frac{mg}{X}$
The time period of the spring-mass system when both the masses $\left(m+M\right)$ are suspended from the spring,
$T=2\pi \sqrt{\frac{(M+m)}{k}}$
$\Rightarrow T=2\pi \sqrt{\frac{\left(m+M\right)X}{mg}}$