Question

The spring as shown in figure is kept in a stretched position with extension $x$. When the system is released, assuming the horizontal surface to be frictionless, the frequency of oscillation is :

• A. $\frac{1}{2\pi }\sqrt{\left[\frac{k(M+m)}{Mm}\right]}$
• B. $\frac{1}{2\pi }\sqrt{\left[\frac{mM}{k(M+m)}\right]}$
• C. $\frac{1}{2\pi }\sqrt{\left[\frac{kM}{m+M}\right]}$
• D. $\frac{1}{2\pi }\sqrt{\left[\frac{km}{M+m}\right]}$

Answer 1

The correct option is A $\frac{1}{2\pi }\sqrt{\left[\frac{k(M+m)}{Mm}\right]}$

$f=\frac{1}{2\pi }\sqrt{\frac{k}{\mu }}$

Where, $\mu =$reduced mass

$=\frac{Mm}{M+m}$
$\therefore f=\frac{1}{2\pi }\sqrt{\frac{k(M+m)}{Mm}}$