First slide

Applications of SHM

Question

A spring has a certain mass suspended from it and its period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

Moderate

A

$\frac{T}{2}$
B

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

$\sqrt{2} T$
D

$2 T$

Solution

$T = 2 π \sqrt{\frac{m}{k}}$ . Also spring constant (k) $\propto \frac{1}{Length (L)}$ , when the spring is half in length, then k becomes twice.
$∴ T^{'} = 2 π \sqrt{\frac{m}{2 k}} \Rightarrow \frac{T^{'}}{T} = \frac{1}{\sqrt{2}} \Rightarrow T^{'} = \frac{T}{\sqrt{2}}$

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