Question

A simple pendulum is 5.90 m long.

(a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 8.15 m/s²?
(b) What is its period if the elevator is accelerating downward at 8.15 m/s²?
(c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 8.15 m/s²?

Answer 1

The period of a simple pendulum changes with the effective gravitational acceleration. Upward acceleration decreases the period while downward acceleration increases it. Horizontal acceleration does not affect the period.

Step-by-step explanation:

The student is asking about the period of a simple pendulum in various scenarios involving different types of acceleration. In each case, the effective gravitational acceleration changes, which will affect the period of the pendulum.

(a) When the elevator accelerates upwards, the effective gravitational acceleration increases, which will decrease the period of the pendulum. (b) Conversely, if the elevator accelerates downwards, the effective gravitational acceleration decreases, increasing the period. (c) When the pendulum is accelerating horizontally, the horizontal acceleration does not affect the vertical motion of the pendulum, so the period remains the same as it would be when the pendulum is at rest provided the angle of swing is less than about 15 degrees. The period of a pendulum is given by the formula T = 2π√(L/g_eff), where L is the length of the pendulum and g_eff is the effective gravitational acceleration.