First slide

Simple hormonic motion

Question

Two springs are connected to a block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant k, the frequency of oscillation of block is

Moderate

A

$\frac{1}{2 π} \sqrt{\frac{k}{2 M}}$
B

$\frac{1}{2 π} \sqrt{\frac{k}{M}}$
C

$\frac{1}{2 π} \sqrt{\frac{2 k}{M}}$
D

$\frac{1}{2 π} \sqrt{\frac{M}{k}}$

Solution

As springs are connected in series, effective force constant
$\frac{1}{k_{eff}} = \frac{1}{k} + \frac{1}{k} = \frac{2}{k} \Rightarrow k_{eff} = \frac{k}{2}$
Hence, frequency of oscillation is
$n = \frac{1}{2 π} \sqrt{\frac{k_{eff}}{m}} = \frac{1}{2 π} \sqrt{\frac{k}{2 M}}$

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