First slide

Periodic Motion

Question

A pendulum suspended from the ceiling of the train has got a time period of two second when the train is at rest. What will be the time period of the pendulum if the train accelerates at 10 m/s²?

Moderate

A

2 s
B

$2 \sqrt{2} s$
C

$(2 / \sqrt{2}) s$
D

none of these

Solution

Net acceleration = $= \sqrt{(a^{2} + g^{2})}$
$= {[(10)^{2} + (10)^{2}]}^{1 / 2} = 10 \sqrt{2} T = 2 π \sqrt{(\frac{l}{10})} = T_{1} = 2 π \sqrt{\{\frac{l}{10 \sqrt{2}}\}} = \{2 π \sqrt{(\frac{l}{10})}\} \frac{1}{(2)^{1 / 4}} = \frac{2}{(2)^{1 / 4}}$

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