When do I use Acosωt and Asinωt for Simple Harmonic Motion?

May 2021 2 72 Report

When do I use Acosωt and Asinωt for Simple Harmonic Motion?

Does it depend upon the way the object is experencing SHM? In the x axis versus the y axis? Or is there no such thing as Asinωt and I am confusing it with something else?

Science & Mathematics / Physics

Steve4Physics

Verified answer

Use sin if the displacement is zero at time zero (and subsequently displacement becomes positive).

So the displacement time graph is like the graph in link 1.

Use cos if the displacement is +A at time zero.

So the displacement time graph is like the graph in link 2.

morningstar

They are equivalent.

cos(wt) = sin(wt + pi/2)

If you think about it, that means the only difference is what time you consider to be t = 0. If at t = 0, the particle is at the extreme of its position, then use cosine. If at t = 0, it's at the center, then use sine.