Question

The position of a body oscillating on a spring is given by x = A sin t, where A and v are constants with values A = 5 cm and  = 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.

Answer 1

a)

$$x=5\sin{0.175t}$$

b)

$$v=0.875\frac{cm}{s}$$

c)

$$v_1=-0.440\frac{cm}{s}\\v_2=-0.118\frac{cm}{s}\\v_3=-0.053\frac{cm}{s}\\ v_4=-0.013\frac{cm}{s}\\v_5=-0.003\frac{cm}{s}\\v_6=-0.0008\frac{cm}{s}\\$$

d)

$$v=0.875\frac{cm}{s}$$