The Angular Displacement $\theta$ Of a Simple Pendulum Is Given By $\theta = \theta _ { 0 } \sin ( \omega t + \phi )$

Essay

The angular displacement $\theta$ of a simple pendulum is given by $\theta = \theta _ { 0 } \sin ( \omega t + \phi )$ where $\theta _ { 0 }$ is the angular amplitude, $\omega$ the angular frequency and $\theta$ a phase constant depending on initial conditions. If we are given that $\omega$ = 10 and $\phi = \frac { \pi } { 2 }$
, find the angular velocity $\frac { d \theta } { d t }$ when $\theta = \frac { \theta _ { 0 } } { 2 }$ .