Which response metric, influenced by damping, measures how quickly a system reaches its peak?

• A. Rise Time
• B. Settling Time
• C. Peak Time
• D. Delay

Answer: (A)

Damping shapes how the transient response behaves, including how quickly the response reaches its first maximum. The metric that captures how fast the system reaches that peak is the peak time—the moment the response first attains its maximum after the start of the input. For a standard underdamped second‑order system, the peak time depends on the damped natural frequency ω_d = ω_n√(1−ζ^2), with the first peak occurring at T_p = π/ω_d. This means more damping lowers ω_d and increases T_p, so the peak takes longer to occur as damping grows.

Rise time, by contrast, measures how long it takes to go from the initial value to the final steady-state value (often 10%–90%), not to the peak. Delay is simply the initial lag before the response starts, and settling time is how long it takes to stay within a small band around the final value. So the metric describing how quickly the peak is reached, and influenced by damping, is peak time.