A particle is exdecuting a linear SHM. What is the nature of the graph between the velocity and displacement of the particle at any ins"tan"t ?

Options

A. a straight line
B. a circle
C. an ellipse
D. a parabola

Answer

C

Explanation

In SHM, displacement ` x= A "sin" omega t`
` therefore (x)/(A)= "sin" omega t`
and velocity `v= A omega "cos" omega t therefore (v)/(A omega)="cos" omega t`
`therefore (x^(2))/(A^(2))+(v^(2))/(A^(2)omega^(2))="sin"^(2)omega t + "cos"^(2) omega t =1`
`therefore` This equation represents an ellipse.