In a transfer function, zeros in the s-domain primarily influence which aspect of the time-domain response?

• A. Zeros primarily scale the DC gain.
• B. Zeros affect natural decay rates.
• C. Zeros affect phase at high frequencies.
• D. Zeros influence the transient shape and overshoot.

Answer: (D)

Zeros in the s-domain shape how the time-domain response behaves in the short term. They come from the numerator of the transfer function and change how the different exponential terms (the effects of the poles) are weighted when you transform back to time. Because of that, zeros mainly affect the transient portion of the response—how quickly the output rises, whether it overshoots the final value, and the overall curvature as the system settles. The long-term steady-state level, on the other hand, is set by the poles (and the gain). Zeros can also shift phase, especially at higher frequencies, but the most noticeable impact in the time domain is on the transient shape and any overshoot.