A uniform rope with length \( L \) and mass \( m \) is held at one end and whirled in a horizont...

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A uniform rope with length \( L \) and mass \( m \) is held at one end and whirled in a horizontal circle with angular velocity \( \omega \). You can ignore the force of gravity on the rope. Find the time required for a transverse wave to travel from one end of the rope to the other.
Hint : \( \int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\sin ^{-1}\left(\frac{x}{a}\right) \)
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