Final answer:
To find the amplitude of the steady-state response to a sinusoidal input in a discrete-time system, we can plug the input function into the ODE and solve for the steady-state response.
Step-by-step explanation:
The given ODE represents a discrete-time system. We are asked to find the amplitude of the steady-state response to the given sinusoid function Xₙ = sin(0.2n). To find the amplitude, we substitute the given input function into the ODE and solve for the steady-state response.
Plugging in Xₙ = sin(0.2n) into the ODE, we get 1.9sin(0.2n) + sin(0.2n-1) = A. We need to solve for A to find the amplitude of the steady-state response.
Once we have the value of A, we can determine the amplitude of the steady-state response.