A simple pendulum of length l hangs from the ceiling of an elevator. Calculate the time period of small oscillations assuming the elevator is going down with an acceleration a₀ .

Step-by-step solution

In the frame of reference of the elevator, a pseudo force m a₀ acts on the pendulum bob in the upward direction, opposite to the downward acceleration of the elevator. The true gravitational force mg acts in the downward direction. The net effective force on the bob is F_ eff = mg - m a₀ = m(g - a₀) . The effective acceleration due to gravity is g_ eff = g - a₀ . The time period of a simple pendulum is given by T = 2 l g_ eff . Substituting the value of g_ eff , we get T = 2 l g - a₀ .