First slide

Applications of SHM

Question

In the 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

$f \times 2$
C

$f \times \sqrt{2}$
D

$f / \sqrt{2}$

Solution

For the given figure $f = \frac{1}{2 π} \sqrt{\frac{k_{eq}}{m}} = \frac{1}{2 π} \sqrt{\frac{2 k}{m}}$ …..(i)
If one spring is removed, then k_eq = k and
$f' = \frac{1}{2 π} \sqrt{\frac{k}{m}}$ ….(ii)
From equation (i) and (ii), $\frac{f}{f^{'}} = \sqrt{2} \Rightarrow f^{'} = \frac{f}{\sqrt{2}}$

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