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  4. A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle θ with horizontal. The time period of pendulum is

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Q. A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle $\theta$ with horizontal. The time period of pendulum is

Oscillations

Solution:

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At equilibrium, inside the trolley, Tension $=m g \cos \theta$ Hence effective $g'=g \cos \theta$
$T=2 \pi \sqrt{\frac{l}{g'}}=2 \pi \sqrt{\frac{l}{g \cos \theta}}$