Question

An object moves with simple harmonic motion of amplitude A and period T. During one complete oscillation, for what length of time is the object's distance from equilibrium greater than A/2? Enter your answer as a formula involving the period.

How much time does it take the object to cover a total distance of 4A? Enter your answer as a formula involving the period.

I've got the first part of the

Answer 1

It takes one period (T) for the object to travel 4A. That's 2A going positive and back to zero, and 2A going negative and back to zero. (Starting at zero)

For the first question, assume

Y = A sin(2 pi t/T)

How much of the time is Y > A/2?

Do the math. Find the times t when y = A/2. The figure out the times when y > A/2, between those points in a single cycle.