Consider the following example:
A particle oscillates with simple harmonic motion in a straight line. In the first $t$ seconds, it travels a distance $a$. In the next 't'$t$ seconds, it travels an additional 2'a'$2a$ distance (in the same direction). Find the time period of oscillation.
For this question, the correct answer only comes when assuming $x=A\cos \omega t$. When using $x=A\sin \omega t$, the answer does not exist. Why?