I have two coupled harmonic oscillators:(adsbygoogle = window.adsbygoogle || []).push({});

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

[tex]\ddot{x}_{2} = kx_{1} - kx_{2}[/tex]

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

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

[tex]X_{1} = \frac{ F(p) + k X_{2} }{ p^{2} + 2k }[/tex]

I then do the same for the second to get

[tex]X_{2} = \frac{ k X_{1} }{ p^{2} + 2k }[/tex]

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

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

My question:

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Transfer Function of Coupled Diff Eq

**Physics Forums | Science Articles, Homework Help, Discussion**