I am given a transfer function of a second-order system as: G(s)=as2+4s+a
and I need to find the value of the parameter a that will make the damping coefficient ζ=.7. I am not sure how to do this but I might have found something that might have helped so I am going to take a stab at it. I found a transfer function in the book of a second order spring-mass-damper system with an external applied force in the book as: G(s)=amω2n(ω2ns2+2ζωn+ω2n)
I was thinking that I could just write ω2n=a and 2ωnζ=4. Then I could just solve for a. Is this possible?
Answer
You have the answer.
Consider 2∗ζ∗ωn=4. ζ=0.7. ω2n=a What value of ωn (or a in your case) satisfies this?
Roughly 8.18 is your answer.
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