A cart connected to a spring oscillates according to the following position equation:

Question

x = 0.20m cos (8 t)
What is the period of this oscillation?
What is the cart's velocity after 4 seconds?

Answer 1

Let P be the period

2 pi/P = 8

P = pi/4

velocity = dx/dt = -1.60 sin(8t) m/s
At t = 4 s,
V(8) = -1.60 sin64 = -1.47 m/s

(The 64 is radians, not degrees)