Question

In shm dot product of instantaneous velocity vector and position vector ??

Answer 1

$$\begin{gathered} Dearstudent \\ lettheshmberepresentedby \\ x\left(t\right)=A\cos (\omega t+\varphi ) \\ v\left(t\right)=-A\omega \sin (\omega t+\varphi ) \\ Lettheanglebetweenbothbe\theta \\ \theta willbedifferentindifferentcasesandtimes \\ dotproduct=-A\cos (\omega t+\varphi )A\omega \sin (\omega t+\varphi )\cos \theta \\ =-A^2\omega \cos (\omega t+\varphi )\sin (\omega t+\varphi )\cos \theta \\ =\frac{2}{2}\left(-A^2\omega \cos (\omega t+\varphi )\sin (\omega t+\varphi )\cos \theta \right) \\ =\frac{-A^2\omega \sin 2(\omega t+\varphi )\cos \theta }{2} \end{gathered}$$