A simple pendulum of length L has been set up inside a railway wagon sliding down a frictionless inclined plane of inclination $\theta$ with the horizontal. Its period of oscillation as recorded by an observer inside the wagon is

The point of suspension has acceleration$\text{a}=\text{g}\sin \theta$  (down the plane) ‘g’ can be resolved into two components$\text{g}\sin \theta$  (along the plane ) and $\text{g}\cos \theta \left({\perp }^{\text{r}}\text{to}\text{plane}\right)$

${\overline{g}}_{\text{eff}}=\overline{g}-\overline{a}=\text{g}\sin \theta \hat{j}+\text{g}\cos \theta \hat{j}-\text{g}\sin \hat{i}$

${\overline{g}}_{\text{eff}}=\text{g}\cos \theta \hat{j}$

$\therefore \text{T}=2\pi \sqrt{\frac{l}{g\cos \theta }}$