Calculate the time period of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle α.

See the following force diagram.Vehicle is moving down the frictionless inclined surface so, its acceleration is gsin⁡α. Since vehicle is accelerating, a pseudo force m(gsin⁡α) will act on bob of pendulum which cancel the sin⁡αcomponent of weight of the bob.Hence net force on the bob is Fnet =mgcos⁡α or net acceleration of the bob is geff=gcos⁡α ∴ Time period T=2πlgefI=2πlgcos⁡α