Transfer Function of Coupled Diff Eq

[dimensionless]

I have two coupled harmonic oscillators:

\ddot{x}_{1} = -2kx_{1} + kx_{2} + f(t)
\ddot{x}_{2} = kx_{1} - kx_{2}

Mass 1 is at position x_{1} and subject to force f(t).

I take the Laplacian of the first equation and solve for X_{1} to get

X_{1} = \frac{ F(p) + k X_{2} }{ p^{2} + 2k }

I then do the same for the second to get

X_{2} = \frac{ k X_{1} }{ p^{2} + 2k }

I then substitute X_{1} into X_{2}, divide out F(p), and then wind up with the transfer function

T(e^{jwt}) = \frac{ z^{-2} + 2kz^{-4} }{ 1 + 4kz^{-2} + 3k^{2}z^{-4} }

My question:

Does this method work for finding the transfer function of coupled differential equations?

 

[quantumdude]

Sure, why not? All you're shooting for is T(p)=X_1(p)/F(p), right? So if you can get there by this method (which you clearly can), then it must work!