Question

differentiate y=r sin(wt-$) where $=phase difference

Answer 1

Given

y=rsin(wt-$0)

let

U=wt-$

du/dt=w...................

y=rsinu.........................dy/du=rcosu............=rcos(wt-$)

from the chain rule

dy/dt=dy/du*du/dt................=rcos(wt-$)*w....................=rwcos(wt-$)

d(rsin(wt-$)/dt=rwcos(wt-$)