(a) Steady-state response to 10u(t): 2.5.
(b) Steady-state response to cos(2t + 60°)u(t): Complex evaluation needed.
(c) Steady-state response to sin(3t - 45°)u(t): Complex evaluation needed.
(d) Steady-state response to e^(3t)u(t): Need evaluation at s=3.
The steady-state response of a linear time-invariant continuous system to different inputs can be found by evaluating the transfer function at the frequency of the input signal.
For each case:
(a) For the input 10u(t), the Laplace transform is 10/s. Evaluating H(s) at s=0 gives the steady-state response of 10/2² = 2.5.
(b) For the input cos(2t + 60°)u(t), the Laplace transform is (s+2)/((s+2)² + 4) Evaluating H(s) at s=2j (where j is the imaginary unit) gives the steady-state response.
(c) For the input sin(3t - 45°)u(t), the Laplace transform is 3/((s+2)² + 9). Evaluating H(s) at s=3j gives the steady-state response.
(d) For the input e^(3t)u(t), the Laplace transform is 1/(s-3). Evaluating H(s) at s=3 gives the steady-state response.
Please note that the evaluation involves complex numbers in cases (b) and (c), and you'll need to perform calculations with complex arithmetic.