Maximum amplitude of second order system

[MMCS]

See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.

 

[collinsmark]

See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.

Okay, so far so good.

But you just sort of stopped. Is there a particular question that you had?

You've already found the derivative of the denominator. Set the derivative equal to 0 and solve for r. You'll find that there are two or three values of r that make the derivative go to 0, but not all of them are necessarily local minimums (there could be local maximums).

Once you find the appropriate expression for r that makes the denominator a minimum, plug that back into |H(jω)| and simplify.