There are two pendulums, one with a shorter string. Thebobs have the same mass,

Question

There are two pendulums, one with a shorter string. Thebobs have the same mass, m, and the pendulums don't interfere witheach other in any way. We pull them both back to the sameheight to start them, and the change in height from the top tobottom of the swing is the same for each. Which pendulum, if either, will reach a greater maximumspeed. I am confused about how to do this. Thought I knew howto do it but got it wrong on the test so am wondering what theright way to do it is. There are two pendulums, one with a shorter string. Thebobs have the same mass, m, and the pendulums don't interfere witheach other in any way. We pull them both back to the sameheight to start them, and the change in height from the top tobottom of the swing is the same for each. Which pendulum, if either, will reach a greater maximumspeed. I am confused about how to do this. Thought I knew howto do it but got it wrong on the test so am wondering what theright way to do it is.

Explanation / Answer

The question is somewhat ambiguos in that it does not statewhether the amplitudes are small or not. As the question is worded, both pendulums would have the samespeed since they are released from the same height. The equation for simple harmonic motion is related to thefrequency by = (k / m) similar to = (L /g) for the simple pendulum and vmax = A    where A isthe "amplitude" of vibration. For simple harmonic motion, the frequency does not depend onthe amplitude, only on the the spring constant and the mass, so the greater the amplitudethe greater the maximum speed. I think the answer wanted is that they both have the samespeed because they both fall thru the same height

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