First slide

Applications of SHM

Question

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio

Moderate

A

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

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

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

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

Solution

$T \propto \frac{1}{\sqrt{k}} \Rightarrow T_{1} : T_{2} : T_{3} = \frac{1}{\sqrt{k}} : \frac{1}{\sqrt{k / 2}} : \frac{1}{\sqrt{2 k}} = 1 : \sqrt{2} : \frac{1}{\sqrt{2}}$

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