Final answer:
Bode plots for the given transfer function are constructed by considering contributions from a zero at the origin and three poles. the magnitude plot combines their slopes, and the phase plot combines their phase shifts at respective frequencies.
Step-by-step explanation:
The question involves sketching the asymptotic Bode plots for the magnitude and phase of a given transfer function H(s) = 80s / (s+10)(s+20)(s+40), where s=jω. Bode plots help us understand the frequency response of a system and are comprised of two plots: one for magnitude (in decibels) and one for phase (in degrees). to construct the Bode magnitude plot, we consider each of the factors of H(s). The zero at the origin contributes +20 dB/decade starting at 0 Hz. Each of the poles contributes -20 dB/decade, starting at their respective frequencies (10 Hz, 20 Hz, and 40 Hz). In constructing the phase plot, the zero contributes +90° phase shift while each pole contributes -90° shift starting from their corner frequencies.
When constructing these plots, we are essentially adding these individual responses. For example, at a high frequency well above 40 Hz, the magnitude slope will be overall -40 dB/decade (since there's one zero and three poles), and the phase shift will be -270° (since three poles each contribute -90°)