Frequency Response

Step 1: Identify the system transfer function.
From the block diagram, the transfer function is:

Step 2: Determine steady-state sinusoidal response.
For input , steady-state output is obtained using frequency response:

Step 3: Evaluate magnitude and phase at .

Step 4: Write steady-state output.

Step 5: Final conclusion.
Thus, the steady-state response of the system is .