Eqn for SHM, sin function, so why cos?

[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)

Halfway down this page:
http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm
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?

 

[Doc Al]

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

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.

 

[ZedCar]

Thank you Doc Al

 

[technician]

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