Assertion: A simple pendulum is suspended from the roof of a trolley, moving freely down a plane of inclination $\theta$ . If the pendulum is displaced from its mean position, the period of oscillation will be $\mathrm{T}=2\mathrm{\pi }\sqrt{\frac{\mathrm{\ell }}{\mathrm{gcos}\mathrm{\theta }}}$
Reason: The axis of mean position is inclined to roof of the trolley.

The trolley moves along the inclined plane with an acceleration $\mathrm{f}=\mathrm{gsin}\mathrm{\theta }$. The bob of the simple pendulum is suspended in the trolley, which is a non-inertial frame of reference.

In the inertial frame of reference of the trolley, a pseudo force is applied on the bob in the opposite direction along the plane. This pseudo force is equal to the rectangular component mg sin $\theta$ acting along the inclined plane. The effective value of force acting perpendicular to the plane and acting downwards will be equal to mg cos $\theta$   in the frame of reference of the trolley.
$\therefore$The effective value of geff is thus equal to g cos  .