Maximum peak overshoot in the time domain corresponds to resonance peak.

Resonance is a phenomenon that occurs in systems with natural frequencies. It is characterized by a peak in the system's response when the excitation frequency matches the natural frequency of the system. In the time domain, this peak is manifested as a maximum peak overshoot.

When a system is excited with a sinusoidal signal at its natural frequency, it undergoes resonance. The amplitude of the system's response increases significantly, resulting in a peak overshoot. This peak overshoot represents the maximum deviation of the system's response from its steady-state value.

Explanation:
To understand why maximum peak overshoot corresponds to resonance peak, let's consider a simple example of a second-order system.

A second-order system can be represented by a transfer function of the form:

H(s) = (ωn^2) / (s^2 + 2ζωns + ωn^2)

where ωn is the natural frequency of the system and ζ is the damping ratio. The natural frequency ωn is related to the resonant frequency fr and the damping ratio ζ by the equation:

ωn = 2πfr√(1 - ζ^2)

When the system is excited with a sinusoidal input signal of frequency fr, the output response will have a peak at the resonance frequency. The magnitude of this peak is determined by the damping ratio ζ. A higher damping ratio results in a smaller peak, while a lower damping ratio leads to a larger peak.

The maximum peak overshoot occurs when the damping ratio ζ is small (close to zero), indicating an underdamped system. In an underdamped system, the response exhibits oscillations before settling to its steady-state value. The maximum peak overshoot is the maximum deviation of the response from its steady-state value.

Therefore, the maximum peak overshoot in the time domain corresponds to the resonance peak because it represents the maximum deviation of the system's response when excited at the natural frequency.