Question

When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.

Options

• Circular

• Elliptical

• Sinusoidal

• Straight line

Answer 1

When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be Elliptical.

Explanation:

For simple harmonic motion, x = A sin ωt

⇒ v = `(dx)/(dt)` = Aω cosωt

`x/A = sinomegat` .............(i)

`"v"/(Aomega) = cosomegat` ..............(ii)

From (i) and (ii) we have,

`(x/A)^2 + ("v"/(Aomega))^2 = sin^2omegat + cos^2omegat`

`(x/A)^2 + ("v"/(Aomega))^2 = 1`

The nature of the graph will be elliptical.