A simple pendulum of length l is attached to the ceiling of an...

In the frame of reference of the elevator accelerating upwards with an acceleration $a_0$, a pseudo force $ma_0$ acts downwards on the pendulum bob of mass $m$.

The true gravitational force $mg$ also acts downwards.

The effective weight of the bob is $W_{\text{eff}} = mg + ma_0 = m(g + a_0)$.

The effective acceleration due to gravity is $g_{\text{eff}} = g + a_0$.

The time period of a simple pendulum is given by $T = 2\pi \sqrt{\dfrac{l}{g_{\text{eff}}}}$.

Substituting the value of $g_{\text{eff}}$, we get $T = 2\pi \sqrt{\dfrac{l}{g + a_0}}$.