Answer:
2.13 h
Explanation:
Simple harmonic motion is:
x = A sin(2π/T t + φ) + B
where A is the amplitude, T is the period, φ is the phase shift, and B is the midline.
This can also be written in terms of cosine:
x = A cos(2π/T t + φ) + B
Here, A = d/2, T = 12.8, φ = 0, and B = d/2. I'll use cosine so that the highest level is at t=0.
x = d/2 cos(2π/12.8 t) + d/2
When x = d - 0.250 d = 0.750 d:
0.750 d = d/2 cos(2π/12.8 t) + d/2
0.250 d = d/2 cos(2π/12.8 t)
0.500 = cos(2π/12.8 t)
π/3 = 2π/12.8 t
12.8/6 = t
t = 2.13
It takes 2.13 hours to fall 0.250 d from the highest level.
