An Algebraic Derivation of the Standing Wave Problem
The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a radial direction using the centripetal force condition. The wave is projected back onto the x,y plane to get the planar time dependent solutions. The allowed frequencies are found for a discrete system as well as a continuous system.
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