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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

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#### Solution

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.

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