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While reading wave motion I encountered the problem of $n$ identical masses with $n$ identical springs in between them.
If we give a sudden push

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to the wall attached to the first spring, what will happen?
I'm confused how to calculate the motion of a mass in this system. Theory says that the disturbance will move in the springs. I'm curious to know how it will propagate in the system (mathematically).
I wonder if the system will have a periodic motion if it is given a push at the starting position.

Lokesh
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  • Related : Eigenvalue equation for kinetic and potential energy. – Frobenius May 19 '22 at 12:37
  • How exactly is the wall moving? If the wall is moved "suddenly" and then stops in its new position, so that the motion of the masses is negligible during the wall's motion, then you can just re-cast it as a problem where all of the masses are moved by a certain amount relative to their (new) equilibrium positions. If the wall moves "slowly", then the oscillation will be negligible. If the motion is comparable to the period of oscillation, then the problem is a good deal harder. – Michael Seifert May 19 '22 at 14:30
  • Wall is moved suddenly, how we can re-cast it as a problem where all of the masses are moved by a certain amount w.r.t. their new equilibrium. How to determine motion of a mth mass as a function of t? – Lokesh May 19 '22 at 15:46

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