First slide

Simple hormonic motion

Question

In figure $S_{1} and S_{2}$ are identical springs. The oscillation frequency of the mass m is f. If one spring is removed, the frequency will become

Moderate

A

f
B

2f
C

$f \sqrt{2}$
D

$\frac{f}{\sqrt{2}}$

Solution

Effective force constant $K_{eff} = 2 K .$
$f = \frac{1}{2 π} \sqrt{\frac{2 K}{a}}$
When one spring is removed, $K_{eff}$ becomes K new frequency
$f^{'} = \frac{1}{2 π} \sqrt{\frac{K}{m}}$
$\frac{f^{'}}{f} = \frac{1}{\sqrt{2}} \Rightarrow f^{'} = \frac{f}{\sqrt{2}}$

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