First slide

Applications of SHM

Question

A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system if a mass 4 m is suspended from the same spring

Moderate

A

$n / 4$
B

$4 n$
C

$n / 2$
D

$2 n$

Solution

$n = \frac{1}{2 π} \sqrt{\frac{k}{m}} \Rightarrow n \propto \frac{1}{\sqrt{m}} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{m_{2}}{m_{1}}}$
$\Rightarrow \frac{n}{n_{2}} = \sqrt{\frac{4 m}{m}} \Rightarrow n_{2} = \frac{n}{2}$

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