When the cart is at rest, the effective acceleration due to gravity is g and when the cart is rolling down the inclined surface, the effective acceleration due to gravity involved perpendicular to plane is g cos θ. Time period of pendulum when art is immobile,
T = \(2\pi\sqrt{\frac{l}{g}}\)
Time period of cart when it moving down the plane,
T’= \(2\pi\sqrt{\frac{l}{g\,cos\,\theta}}\)
Or T' = \(\frac{T}{\sqrt {cos \theta}}\)