Question

A mass $M$ is suspended from a mass less spring. An additional mass $m$ stretches the spring further by a distance $x,$ The combined mass will oscillate with a period:

• A. $2\pi \sqrt{\left\{\frac{(M+m)x}{mg}\right\}}$
• B. $2\pi \sqrt{\left\{\frac{mg}{(M+m)x}\right\}}$
• C. $2\pi \sqrt{\left\{\frac{(M+m)}{mgx}\right\}}$
• D. $\frac{\pi }{2}\sqrt{\left\{\frac{mg}{(M+m)x}\right\}}$

Answer 1

The correct option is A $2\pi \sqrt{\left\{\frac{(M+m)x}{mg}\right\}}$

$mg=kx$
$\therefore$ $k=\frac{mg}{x}$
$T=2\pi \sqrt{\frac{M+m}{k}}=2\pi \sqrt{\frac{(M+m)x}{mg}}$