The problem is the following:(adsbygoogle = window.adsbygoogle || []).push({});

a.) Obtain the equation of motion for the very small oscillations of a bead of mass m

attached 1/5th of the way along a massless string of length 5l, which is under tension T.

b.) Hence show that the angular frequency of oscillation is omega=sqrt(5T/4ml)

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Now, i would start looking at this problem by looking at the problem by observing the following relation:

Force = -spring constant * displacement = mass * angular frequency of oscillation squared * displacement

That is:

F = -sx = mx omega^2

Now, presumably force F can be substituted by tension T. This however is where i start to run into trouble. Normally, to calculate the equation of motion for a SHO i would start by calculating omega, and the amplitude and use that to calculate the equation of motion. However this question seems to want me to do the exact opposite.

I also am not sure how to calculate omega as, although i am given the length of the string, i am given neither its spring constant, nor the amplitude of vibration of the bead.

In fact the question does not even specify whether the bead is oscillating along the length of the string, in which case the string would behave as two springs, or perpendicularly.

As you can see i am very lost and help to put me on the right track would be appreciated.

Thanks

Chopo

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# Simple Harmonic Oscillator

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