A pendulum of length l is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is t. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

The period of the pendulum will increase.

Explanation:

The period of the pendulum will increase since g efective will decrease.

Then g efective is given by

g efective = g - a < g

If ⇒  T = 2π√(L/g)

and T' = 2π√(L/(g - a))

then  T < T'

When the elevator accelerates downward, the hanging mass  feels “lighter” – this means that the effective value of g has  decreased due to the acceleration of the elevator. Since the  period depends inversely on g, and the effective value of g  decreased, then the period of the pendulum will increase .

(i.e., its frequency will decrease and it will swing slower)

a and b sometimes have a positive value