Explain what is phase and draw a single graph showing different phases of simple harmonic motion.

(N/A) The position of a particle in simple harmonic motion $(SHM)$ is given by the equation $x(t) = A \cos(\omega t + \phi)$,where $t$ is time. The argument $(\omega t + \phi)$ is called the phase of the motion at time $t$. It determines the state of motion (position and direction) of the oscillator at that instant.
Phase constant (Initial phase): At time $t = 0$,the phase of the simple harmonic oscillator is $\phi$,which is known as the initial phase or phase constant.
If the amplitude $A$ is fixed,the initial phase $\phi$ can be determined from the displacement of the particle at $t = 0$:
$x(0) = A \cos(\phi)$
$\therefore \cos \phi = \frac{x(0)}{A}$
$\therefore \phi = \cos^{-1}\left(\frac{x(0)}{A}\right)$
The graph shows two curves representing $SHM$ with different phases. Curve $3$ corresponds to $\phi = 0$,and curve $4$ corresponds to $\phi = -\frac{\pi}{4}$. Both curves have the same amplitude $A$.