Question

An object attached to a coiled spring is pulled down a distance of 10 centimeters from its rest position and then released.

Assuming that the motion is simple harmonic
with a period of 2 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds.

Also assume that the positive direction of
the motion is up. At time t=0 the object is at its resting position and moving down.

Answer 1

Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Explanation: