First slide

Simple hormonic motion

Question

Five identical springs are used in the three configurations as shown in figure. The ratio of frequencies of oscillations in the given three configurations respectively is

Moderate

A

$1 : \sqrt{2} : \frac{1}{\sqrt{2}}$
B

$\sqrt{2} : 1 : \frac{1}{\sqrt{2}}$
C

$1 : \frac{1}{\sqrt{2}} : \sqrt{2}$
D

$2 : \frac{1}{\sqrt{2}} : 1$

Solution

$\begin{array}{l} T h e frequency of oscillation f = \frac{1}{T} = \frac{1}{2 π} \sqrt{\frac{k_{e q}}{m}} \\ H e n c e, \\ f_{a} = \frac{1}{2 π} \sqrt{\frac{k}{m}} \\ f_{b} = \frac{1}{2 π} \sqrt{\frac{k / 2}{m}} \\ f_{c} = \frac{1}{2 π} \sqrt{\frac{2 k}{m}} \\ f_{a} : f_{b} : f_{c} = 1 : \frac{1}{\sqrt{2}} : \sqrt{2} \end{array}$

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