Final answer:
The analytical frequency response of the transfer function G(s) = 200(s + 2) / (s^2 + 30s) can be found by substituting the complex variable s with jω. The magnitude of the frequency response is sqrt((200^2*(ω^2 + 4)) / (ω^4 + 60^2ω^2)), and the phase is atan2(2ω, -ω^2 - 30iω).
Step-by-step explanation:
The analytical frequency response of a transfer function can be obtained by substituting the complex variable s with jω, where j represents the imaginary unit and ω is the angular frequency. In this case, the transfer function G(s) = 200(s + 2) / (s^2 + 30s) can be written as G(jω) = 200(jω + 2) / (j^2ω^2 + 30jω).
To find the magnitude of the frequency response, we substitute jω with iω, where i is the imaginary unit. Then, we have G(iω) = 200(iω + 2) / (-ω^2 - 30iω). The magnitude of the frequency response is given by |G(iω)| = sqrt((200^2*(ω^2 + 4)) / (ω^4 + 60^2ω^2)).
To find the phase of the frequency response, we take the argument of G(iω), which is given by arg(G(iω)) = atan2(2ω, -ω^2 - 30iω).