First slide

Applications of SHM

Question

A mass m performs oscillations of period T when hanged by spring of force constant K. If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be

Moderate

A

2T
B

T
C

$\frac{T}{\sqrt{2}}$
D

$\frac{T}{2}$

Solution

$T \propto \frac{1}{\sqrt{k}} \Rightarrow \frac{T_{2}}{T_{1}} = \sqrt{\frac{K_{1}}{K_{2}}} = \sqrt{\frac{k}{4 k}} = \frac{1}{2} \Rightarrow T_{2} = \frac{T_{1}}{2}$

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