Question

A certain system has a transfer function in the Laplace domain given by

H(s) = = S/(S+S1) (S+S2)'

where s₁ = 2007 and s₂ = 20,000π
a. Find the transfer function, H (w) = H(S)\s=jw

Answer 1

The goal is to convert the Laplace domain transfer function H(s) to the frequency domain transfer function H(w) by replacing s with jw for a given system with specific values for s1 and s2.

Step-by-step explanation:

The question asks to find the transfer function H(w) given the transfer function H(s) in the Laplace domain, where s is a complex variable. For this specific system, the Laplace domain transfer function is provided as H(s) = S/(S+S1)(S+S2), with values for s1 and s2 given as 2007 and 20,000π respectively.

To find the transfer function in the frequency domain, H(w), you need to substitute s with jw (where j is the imaginary unit and w represents the angular frequency) in the Laplace domain transfer function. This results in H(jw) = jw/((jw+2007)(jw+20000π)), which is the frequency response of the system.