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 $\alpha$

As shown in the figure, acceleration down the plane 

$\mathrm{a}=\mathrm{g} \sin \mathrm{\alpha }$ is the pseudo acceleration applied by the observer in the accelerated frame

$\mathrm{The} \mathrm{effective} \mathrm{acceleration} \mathrm{of} \mathrm{the} \mathrm{bob} \mathrm{is} \mathrm{gcos\alpha }$

$\mathrm{so} \mathrm{time} \mathrm{period} \mathrm{of} \mathrm{oscillation}$

$T=2\pi \sqrt{\frac{L}{g\cos \alpha }}$