First slide

Applications of SHM

Question

If a spring has time period ‘T’ and cut into ‘n’ equal parts then the time period of each part will be

Moderate

A

$T \sqrt{n}$
B

$\frac{T}{\sqrt{n}}$
C

$n T$
D

$T$

Solution

Given $T_{1} =T$ , force constant is
$K_{1} =K$
force constant of each spring after cutting into n parts is
$K_{2} =nK$
time period of mass attached to cut spring
$T_{2} =?$
time period of mass attached to a spring is
$T = 2 π \sqrt{\frac{m}{k}} T_{1} α \frac{1}{\sqrt{K_{1}}} T_{2} α \frac{1}{\sqrt{K_{2}}}$
$\frac{T_{1}}{T_{2}} = \sqrt{\frac{K_{2}}{K_{1}}}$
$\frac{T}{T_{2}} = \sqrt{\frac{nK}{K}}$
$\frac{T}{T_{2}} = \sqrt{\frac{n}{1}} \Rightarrow T_{2} = \frac{T}{\sqrt{n}}$

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