Draw plots for initial phase $\phi = 0$ for different periods.

(N/A) The general equation for simple harmonic motion is $x(t) = A \sin(\omega t + \phi)$.
Given the initial phase $\phi = 0$,the equation becomes $x(t) = A \sin(\omega t)$.
This represents a sine wave starting from the origin at $t = 0$. However,if the motion starts from the extreme position,the equation is $x(t) = A \cos(\omega t)$.
The provided graph shows displacement versus time for two different periods.
In this plot,curve $(b)$ has half the period $(T_b = T_a / 2)$ and twice the frequency $(f_b = 2f_a)$ compared to curve $(a)$.