Question

Write an equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilibrium, bounces to it maximum height of 6 inches above equilibrium and returns to its lowest point in a total of 2 seconds. (think about amplitude and period)

Answer 1

So a general harmonic equation is Asin(2πt/T). Little t is just a variable. 6 inches is the height of one maximum and one minimum from equilibrium, so that is the amplitude A. T is the period, or the time of one cycle (or wavelength), which is 2 seconds.

The equation is therefore (in terms of seconds and inches), 6*sin(2πt/2), or 6*sin(πt).