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## Homework Statement

Show that v_max = w_max * Length of string where v_max is the velocity of the simple pendulum and w_max is the maximum angular velocity.

## Homework Equations

[itex]\omega_{velocity} = -\theta_{max} \cdot \omega_{frequency} \cdot sin(\omega_{frequency} \cdot t + \phi)[/itex]

## The Attempt at a Solution

The closest resemblance I could find was using energy:

[itex]\frac{1}{2}kx^2 = \frac{1}{2}mv_{max}^2[/itex] where x = some displacement. The displacement in this pendulum's clase would be the Length of the string * angular displacement because s = Lθ.

Solving for v_max gives: [itex]v_{max} = \omega_{frequency} \cdot x[/itex]

But the 'x' in this case represents the displacement made by the pendulum (the arclength subtended by the angular displacement).

Is there another equation I'm unaware of?