A seconds pendulum is suspended from the ceiling of an elevator that is initially at rest. The elevator then starts moving upwards with a constant acceleration of g 3 , where g is the acceleration due to gravity. What will be the new time period of the pendulum?

Step-by-step solution

The time period of a seconds pendulum at rest is T = 2 s. The formula for the time period of a simple pendulum is T = 2 L g . When the elevator accelerates upwards with an acceleration a = g 3 , the frame of reference is non-inertial. The effective acceleration due to gravity becomes: g_ eff = g + a = g + g 3 = 4g 3 The new time period T' is given by: T' = 2 L g_ eff Taking the ratio of the new time period to the original time period: T' T = g g_ eff Substituting g_ eff = 4g 3 and T = 2 s: T' 2 = g 4g 3 = 3 4 = 3 2