$\vec r = (\sin \,t\,\hat i\, + \,\cos \,t\,\hat j\, + \,t\,\hat k)m$
Find time $'t'$ when position vector and acceleration vector are perpendicular to each other

$y_1 = \sin \left( {\omega t + \frac{\pi }{3}} \right)$ and $y_2 = \sin \omega t$ is :
where $A$ and $p$ are constant.
The period of small oscillations of the particle is