Understanding Transfer Functions in ODEs

incognitor
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Hi,

I am undertaking an undergrad design project and want to ensure I'm doing this correctly,

I have derived the ODE as shown below;

A*Y = M*X'' + (B+C)*X' + D*X
Where A,M,B,C,D are constants.

By taking the Laplace transform, I get;
A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s)

Therefore,
My transfer function becomes;

TF(s) = X(s)/Y(s) = the image of the transfer function below;
http://imageshack.us/a/img37/8820/95533304.jpg


Am I correct here?
 
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