Question

A mass M is suspended from a massless 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 $2\pi \sqrt{\left\{\frac{(M+m)x}{mg}\right\}}$

$kx=mg\Rightarrow k=\frac{mg}{x}$

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

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