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The set up is a pendulum of length 2m with a mass on the end at 0.5kg. The mass is released at a small initial angle of 6 degrees moving into harmonic motion.

I need to calculate the angular frequency of the oscillations and the maximum velocity then I need to know how the velocity changes if the mass is doubled to 1kg or if the rope length was doubled to 4m.

I need to know how to calculate angular frequency and maximum velocity but then it would be nice if a change in the mass or rope length has a corresponding change in the maximum velocity. If it does, please say but if it doesn't then don't answer that part, I will calculate those myself if you explain how.

Penny
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  • You have amplitude = $l \theta=2 * 6*\frac{\pi}{180}$ and $v_{max}= A \omega = \frac{2\pi A}{T}$ where $T=2 \pi \sqrt{\frac{l}{g}}$ – Nikunj Apr 29 '16 at 09:31

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Hint:

use the conservation of energy, noting that the kinetic energy is $E_k=\frac{1}{2}mv^2$ and the variation of the potential energy is $\Delta E_p=mgl-mgl\cos \theta$ where $\theta$ is the displacement angle.

So you can see that the maximum velocity does not depend from the mass, but it is proportional to the square root of the lenght $l$.

Emilio Novati
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Have a look at this page http://arachnoid.com/gravitation_equations/pendulum.html.

The mass has no effect on the pendulum its motion is dependent on the length (L) and the acceleration due to gravity (g).

James Screech
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