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

$m a s s s p r i n g a t t a c h e d t o a s p r i n g t i m e p e r i o d = T = 2 π \sqrt{\frac{m}{k}} - - - (1) if a spring is cut into n equal parts then new spring constant of each part k^{1} = nk time period of each part = T^{1} = 2 π \sqrt{\frac{m}{k^{1}}} = 2 π \sqrt{\frac{m}{nk}} - - - - (2) divide eqn (2) by (1) \frac{T^{1}}{T} = \frac{2 π \sqrt{\frac{m}{nk}}}{2 π \sqrt{\frac{m}{k}}} \frac{T^{1}}{T} = \frac{1}{\sqrt{n}} T^{1} = \frac{T}{\sqrt{n}}$

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