# Eqn for SHM, sin function, so why cos?

1. Dec 20, 2011

### ZedCar

I had thought the eqn of simple harmonic motion is a sinusoidal function of time, with the eqn being:

x(t) = A sin(wt + ∅0)

http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm [Broken]
in Problems:

in solution (a) it gives;

The displacement as a function of time is x(t) = Acos(ωt + φ).

Why are they using a cos and not a sin function?

Last edited by a moderator: May 5, 2017
2. Dec 20, 2011

### Staff: Mentor

Which one you use is arbitrary. Realize that the only difference between the two is a phase factor. (Shift a sine function by 90° and it becomes a cosine function.)

Using x = Acosωt just implies that you are starting the clock when the object is at its maximum displacement. Using x = Asinωt implies that you are starting the clock when the object passes the equilibrium point.

Just two completely equivalent ways of describing the same thing.

3. Dec 20, 2011

### ZedCar

Thank you Doc Al

4. Dec 20, 2011

### technician

Doc Al has said it..... you will not hear a more straightforward explanation