- #1
mpm
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I am in a Systems and Vibrations class but am currently doing differential equations.
A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots.
So far I have:
X(s)/F(s) = (6s +4)/(s^2+14s+58)
That is the transfer function but now i have to find the roots.
I realize I only concern myself with the s^2+14s+58 part and set it equal to 0.
I can't factor it because of obvious reasons. I tried the quadratic equation but my calculator says its a non-real result which means its complex.
My problem is that I can't figure out how to do the quadratic when there is a complex root.
I know as^2 + bs + c = a[(s + sigma)^2 + omega^2] = 0.
However, I can't figure out how to find the roots using this equation.
Cany anyone help me with this?
Thanks,
Mike
A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots.
So far I have:
X(s)/F(s) = (6s +4)/(s^2+14s+58)
That is the transfer function but now i have to find the roots.
I realize I only concern myself with the s^2+14s+58 part and set it equal to 0.
I can't factor it because of obvious reasons. I tried the quadratic equation but my calculator says its a non-real result which means its complex.
My problem is that I can't figure out how to do the quadratic when there is a complex root.
I know as^2 + bs + c = a[(s + sigma)^2 + omega^2] = 0.
However, I can't figure out how to find the roots using this equation.
Cany anyone help me with this?
Thanks,
Mike