The time period of the elevator moving downwards with an acceleration of 8 m/s² is approximately 2.83 seconds.
To find the time period of the elevator, we need to first understand that the time period of an object moving in simple harmonic motion is the time taken for one complete cycle. In this case, the elevator is moving downwards with an acceleration of 8 m/s². The time period can be found using the formula:
Time period = 2π√(a/g)
Plugging in the values, we get:
Time period = 2π√(8/9.8) ≈ 2.83 seconds