# Which equation to use for simple harmonic motion?

I recently started studying simple harmonic motion and I came across two equations for the displacement of a particle, as given in my textbook:

\begin{align} y &= a\sin(\omega t +\phi)\\ x &= a\cos(\omega t+ \phi) \, . \end{align}

I really have no clue when to use which one. It would help me a lot if someone could give an explanation on this.

$$\cos(\omega t+\phi)=\sin(\omega t+\phi-\pi/2)$$
• @UserKunal123 No, the sign of $\omega$ will change. $\phi$ defines the starting point of the oscillation. – probably_someone Jan 10 '20 at 18:40
• For the equation $y=A\sin(\omega t-\phi)$, the starting position is positive if $\phi$ is positive. For the equation $y=A\sin(\omega t+\phi)$, the starting position is negative if $\phi$ is positive. Once again, you can use either one. – probably_someone Jan 10 '20 at 18:55
• @UserKunal123 Yes, the numbers you plug in to $\omega$ and $\phi$ would be different in every case, but you can use any of them. – probably_someone Jan 10 '20 at 19:10