SHM cos和sin的問題

This depends on the initial condition. That is, the displcement of the object at time t = 0

The general equation describing an object performing simple harmonic motion is,
x = A.sin(wt + p)
where x is the displacement of the object at time t
w is the angular frequency of oscillation
A is the amplitude of oscillation
p is a phase angle, which indicates the "phase" at time t =0. Its value can be found using the dispalcement condition at t = 0.

If at t = 0, the object is at the equilibrium position, we have x = 0, then
0 = A.sin(w(0) + p)
i.e. 0 = A.sin(p)
sin(p) = 0
thus p = 0
The equation becomes: x = A.sin(wt)

On the other hand, if the object is at an extreme position ( x = A) at t = 0, then
A = A.sin(w(0) + p)
i.e. sin(p) = 1
p = pi/2 ( pi = 3.14159...)
The equation thus becomes,
x = A.sin(wt + pi/2) = A.cos(wt)

Therefore, the choice of equation, wether to use sine or cosine, depends on the position of the object at t = 0.