Let the angle of the incline be $\alpha$. The cart accelerates down the incline with $a = g \sin\alpha$. In the non-inertial frame of the cart, the pendulum bob is subject to an effective gravitational acceleration $\vec{g}_{eff}$, which is the vector difference between the true gravitational acceleration $\vec{g}$ and the frame's acceleration $\vec{a}$.

$$ \vec{g}_{eff} = \vec{g} - \vec{a} $$

Resolving these vectors into components perpendicular and parallel to the incline, the parallel components cancel ($g \sin\alpha - a = 0$), while the perpendicular component of $\vec{g}_{eff}$ is due only to $\vec{g}$ ($g \cos\alpha$). The magnitude of the effective gravity is therefore $g_{eff} = g \cos\alpha$. The period of a pendulum depends on the effective gravity: $T = 2\pi\sqrt{L/g_{eff}}$. The period on the immobile cart is $T_0 = 2\pi\sqrt{L/g}$. The new period on the accelerating cart is:

$$ T = 2\pi\sqrt{\frac{L}{g \cos\alpha}} = \left(2\pi\sqrt{\frac{L}{g}}\right) \frac{1}{\sqrt{\cos\alpha}} = \frac{T_0}{\sqrt{\cos\alpha}} $$

Since $\cos\alpha \le 1$, the period $T$ will be greater than or equal to $T_0$.