Question

VELOCITY AND ACCELERATION
16.A particle executes SHM in a straight line.The maximum speed of the particle during its motion is V_m, then the average speed of the particle during its SHM is -----------------

Answer 1

$$\begin{gathered} IftheequationofmotionofSHMis \\ y=A\sin \omega t \\ thenmaximumspeed=V\left(t\right)=A\omega \cos \omega twhen\cos \omega =1 \\ thereforeV\left(t\right)=V_m\cos \omega t \\ So,averagespeedoveroscillation \\ =averagespeedinaquateroscillation \\ =1/\left(4T\right)\times {\int }_0^{T/4}{V}_m\cos \omega tdt \\ =(4V_m/2\pi )\times \sin (\pi /2) \\ =\frac{2_{}{V}_m}{\pi }m/s \end{gathered}$$