- #1

- 463

- 1

[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?