(a) For a particle moving in simple harmonic motion, the position can be written x(t) = xm...

Question:

(a) For a particle moving in simple harmonic motion, the position can be written x(t) = xm cos wt. What is the velocity vx(t) as a function of time for this particle?
(b) Using the small-angle approximation for the sine function, find the slope of the graph of Φ(t) = Φ0 sin wt at t = 0. Does your result agree with the value of ΔΦ/Δt = wΦ0 cos wt at t = 0?