NCoupled Oscillators

1
N-Coupled Oscillators
m
h
xj
xj-1
xj1
Try
Eigenvalue equation
2
Sinusoidal X Solution
Mass at j0 and jN fixed
Try form
For Xj0 at N
3
Sinusoidal Solution (pictures)
4
Initial Conditions for N Particles
Initially let each particle be at rest but
displaced XjXj(0)
Matrix inversion
Solution
5
Vertical Displacements
q
q-
yj
h
Assume small angles
Same equation as before