Please help me with this Trigonometry harmonic motion Question...?

Question

Q: A weight hangs from the end of a spring at its rest position. The weight is then pulled down 4 inches and released. The subsequent motion of the weight is given by an equation of the form
y = AcosBt,
where t represents time in seconds and y is the displacement in inches of the weight relative to the rest position. Find A and B if the time at which the weight first returns to the rest position is t=2.


I am able to find A, but I don't know how to find B. I came up with 2pi/3, but the correct answer is pi/4. I don't understand how this is reached. Can someone please explain to me how to answer this? Thank you very much.

Answer 1

When y = -4 , t = 0 so -4 = A
When t = 2 y = 0 , so 0 =Acos2B = -4cos2B
cos 2B = 0 --> 2B = pi/2 --> B= pi/4
So y = -4cospi*t/4