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 $α$ , is given
by

Difficult

A

$2 π \sqrt{\frac{L}{g \cos α}}$
B

$2 π \sqrt{\frac{L}{g \sin α}}$
C

$2 π \sqrt{\frac{L}{g}}$
D

$2 π \sqrt{\frac{L}{g \tan α}}$

Solution

See the following force diagram.
Vehicle is moving down the frictionless inclined surface so, it's acceleration is g sin $θ$ sin. Since vehicle is accelerating, a pseudo force m(g sin $θ$ ) will act on bob of pendulum which cancel the sin0 component of weight of the bob. Hence net force on the bob ts F_net= mg cos $θ$ or net acceleration of the bob is g_eff= g cos $θ$
$∴ Time period T = 2 π \sqrt{\frac{l}{g_{e f f}}} = 2 π \sqrt{\frac{l}{g \cos θ}}$

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