First slide

Simple hormonic motion

Question

In the figure all springs are identical having spring constant k and mass m each. The block also has mass m. The frequency of oscillation of the block is

Moderate

A

$\frac{1}{2 π} \sqrt{\frac{3 k}{m}}$
B

$\frac{1}{2 π} \sqrt{\frac{3 k}{2 m}}$
C

$2 π \sqrt{\frac{3 m}{3 k}}$
D

none of these

Solution

If spring has the mass then:
$f = \frac{1}{2 π} \sqrt{\frac{k}{m + \frac{M_{spring}}{3}}}$
Spring equivalent = 3k (As all are in parallel)
$f = \frac{1}{2 π} \sqrt{\frac{3 k}{m + \frac{(3 m)}{3}}} \Rightarrow f = \frac{1}{2 π} \sqrt{\frac{3 k}{2 m}}$

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