First slide

Applications of SHM

Question

The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $θ$ , is given by

Moderate

A

$2 π \sqrt{\frac{L}{gcos θ}}$
B

$2 π \sqrt{\frac{L}{gsin θ}}$
C

$2 π \sqrt{\frac{L}{g}}$
D

$2 π \sqrt{\frac{L}{gtan θ}}$

Solution

See the following force diagram.
Vehicle is moving down the frictionless inclined surface so, it's acceleration is $gsinθ$ . Since vehicle is accelerating, a pseudo force $m (gsinθ)$ will act on bob of pendulum which cancel the $sinθ$ component of weight of the bob.
Hence net force on the bob is F_net $= mgcosθ$ or net acceleration of the bob is $g_{eff} = gcosθ$
$∴$ Time period $T = 2 π \sqrt{\frac{L}{g_{eff}}} = 2 π \sqrt{\frac{L}{gcosθ}}$

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