Solution:

In simple harmonic motion (SHM), the velocity \( v \) and displacement \( x \) of a particle are related by:

\[
v = \pm \sqrt{\omega^2 A^2 - \omega^2 x^2}
\]

where:
- \( \omega \) is the angular frequency,
- \( A \) is the amplitude.

 Solution:

1. Rearranging this equation, we get:
\[
\frac{v^2}{\omega^2 A^2} + \frac{x^2}{A^2} = 1
\]

2. This is the equation of an ellipse in the \( v \)-\( x \) plane.

Answer:
The graph of velocity as a function of displacement for a particle in SHM is an ellipse.