Question

An object is in simple harmonic motion with the equation of motion as x=Acos(ωt+φ),when t=T/2,the velocity of the object is......?

Answer 1

Gives

$x=Acos(wt+\phi)\rightarrow(1)$

A=amplitude

Phase=$\phi$

Angular frequency=w

equation (1) differencuate with respect time

Velocity

$v=Awsin(wt+\phi)$

t=0

$v=Awsin\phi\rightarrow(2)$

$t=\frac{T}{2}$

$v=Awsin(\frac{2\pi}{T}\times\frac{T}{2}+\phi)$

$v=Awsin(\pi+\phi)$

$v=Awsin\phi\rightarrow(2)$

equation (2)and(3)are same

Point P wave equation

$t=\frac{T}{2}$ Velocity of object

$v=Asin\phi$