Control and systems — response types In system analysis, the output observed when a sinusoidal input is applied is termed the system’s __________ response.

Introduction / Context:
Characterizing a system’s behavior under different standard test inputs (impulse, step, sinusoid) is central to control theory and signal processing.

Given Data / Assumptions:

• Sinusoidal inputs probe how a system attenuates and phase-shifts various frequencies.
• The steady-state sinusoidal output defines gain and phase as a function of frequency.

Concept / Approach:
The term frequency response describes output amplitude and phase versus input frequency. It is typically visualized with Bode plots, Nyquist plots, or frequency response functions that guide stability and performance design.

Step-by-Step Solution:
Recognize input type: sinusoidal → frequency domain characterization.Match terminology: “frequency response.”Exclude impulse and step, which correspond to other canonical tests.

Verification / Alternative check:
Any LTI system driven by a sinusoid has a sinusoidal steady-state output whose amplitude and phase define the frequency response at that frequency.

Why Other Options Are Wrong:

• Impulse response: output to a Dirac-like impulse; relates to system’s time-domain kernel.
• Unit step response: output to a Heaviside step; used to assess rise time, overshoot, settling.
• None of these: incorrect because “frequency response” is the standard term.

Common Pitfalls:

• Mixing time-domain and frequency-domain nomenclature.

Final Answer:
frequency