_alexis_
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While trying to solve a problem in physics I got this system of 3, second order differential equations.
Solution should be equation for linear harmonic oscillator.
m\ddot{η}1+kη1-kη2=0
mn\ddot{η}2-kη1+2kη2-kη3=0
m\ddot{η}3-kη2+kη3=0
My attempts at the solution produced 6th order equation that I only manage to reduce to 4th order but after that I got completely lost.
Here is what I did if you wish to see: part1 part2
Solution should be equation for linear harmonic oscillator.
m\ddot{η}1+kη1-kη2=0
mn\ddot{η}2-kη1+2kη2-kη3=0
m\ddot{η}3-kη2+kη3=0
My attempts at the solution produced 6th order equation that I only manage to reduce to 4th order but after that I got completely lost.
Here is what I did if you wish to see: part1 part2