Final answer:
The question involves calculating the steady-state response y(t) of a system given an input function f(t) and frequency response H(ω), which is a typical signal processing problem in engineering.
Step-by-step explanation:
The question deals with the determination of the steady-state response y(t) of a system given an input f(t) and its frequency response H(ω). This requires the use of concepts from signal processing and systems engineering, specifically involving Fourier Transform and the response of systems to complex exponential inputs. To find the steady-state response, one must apply the input signal to the given frequency response and use inverse Fourier Transform, ensuring the result is expressed with real-valued signals only. The use of Euler's formula, trigonometric identities, and possibly phasor representation would be involved in this process. The input signal must be broken down into its constituent frequency components, which are then individually passed through the system's frequency response. The outputs for these components are then combined to form the total response y(t).