The position of a body oscillating on a spring is given by x = A sin wt, where A and w are constants with values A = 5 cm and w =0.175 s^-1.

(a) Sketch x versus t for 0 ≤ t ≤ 36 s.

(b) Measure the slope of your graph at t = 0 to find the velocity at this time. 

(c) Calculate the average velocity for a series of intervals beginning at t = 0 and ending at t = 6, 3, 2, 1, 0.5, and 0.25 s. 

(d) Compute dx/dt and find the velocity at time t = 0.