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 givenby

See the following force diagram.Vehicle is moving down the frictionless inclined surface so, it's acceleration is g sinθ sin. Since vehicle is accelerating, a pseudo force m(g sinθ) will act on bob of pendulum which cancel the sin0 component of weight of the bob. Hence net force on the bob ts Fnet= mg cosθ or net acceleration of the bob is geff= g cosθ ∴ Time period T=2πlgeff=2πlgcos⁡θ