The velocity v and displacement x of a particle executing simple harmonic motion are related as
`v (dv)/(dx)= -omega^2 x`.
`At x=0, v=v_0.` Find the velocity v when the displacement becomes x.

Explanation

To solve the problem, we start with the given relationship between velocity \( v \) and displacement \( x \) for a particle executing simple harmonic motion:

\[ v \frac{dv}{dx} = -\omega^2 x \]

### Step 1: Rearranging the Equation
We can rearrange the equation to separate variables. This gives us:
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