First slide

Simple hormonic motion

Question

Two springs of force constants K and 2K are connected to a mass as shown below. The frequency of oscillation of the mass is

Easy

A

$(\frac{1}{2 π}) \sqrt{(\frac{K}{m})}$
B

$(\frac{1}{2 π}) \sqrt{(\frac{2 K}{m})}$
C

$(\frac{1}{2 π}) \sqrt{(\frac{3 K}{m})}$
D

$(\frac{1}{2 π}) \sqrt{(\frac{m}{K})}$

Solution

$n = \frac{1}{2 π} \sqrt{\frac{K_{effective}}{m}}$
Springs are connected in parallel
$K_{eff} = K_{1} + K_{2} = K + 2 K = 3 K$
$\Rightarrow n = \frac{1}{2 π} \sqrt{\frac{(K + 2 K)}{m}} = \frac{1}{2 π} \sqrt{\frac{3 K}{m}}$

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