Final answer:
To find the steady-state system response for different inputs, we need to substitute each input into the transfer function and solve for the system response.
Step-by-step explanation:
To find the steady-state system response for different inputs, we need to substitute each input into the transfer function and solve for the system response. Let's go through each input:
(a) For the input 10u(t), we substitute 10 for u(t) in the transfer function and simplify the expression.
(b) For the input bcos(2t) + 60u(t), we substitute bcos(2t) + 60 for H(s) in the transfer function and simplify the expression.
(c) For the input sin(3t) - 45u(t), we substitute sin(3t) - 45 for H(s) in the transfer function and simplify the expression.
(d) For the input dej(3i)u(t), we substitute dej(3i) for H(s) in the transfer function and simplify the expression.
The steady-state response of an LTIC system with transfer function H(s) can be found by applying each input to the system and analyzing the output in the frequency domain using the final value theorem and checking for stability and resonance.
Finding the Steady-State Response of an LTIC System
To find the steady-state response of an LTIC (Linear Time-Invariant Continuous-time) system described by the transfer function H(s) = (s + 3)/(s + 22), we apply the input to the system and analyze the output in the frequency domain. Given inputs to the system are (a) a step function, (b) a cosine function, (c) a sine function, and (d) an exponential function with a step. We will use the concept of the final value theorem to determine the steady-state response for these inputs.
For the step input 10u(t), the system will reach a new steady state value that can be computed by evaluating H(s) as s approaches zero. This is assuming that the system is stable and the poles of the transfer function are in the left half of the s-plane. For the cosine and sine inputs, we should consider the frequency response of the system and check whether there's resonance at the frequencies given. Lastly, for the exponential input, the response will depend on the stability of the system to this particular input frequency. It is important to calculate the magnitude and phase of the output at each given frequency for a complete response.
It is important to note that steady-state response only occurs if the system reaches an equilibrium after transient effects have died down. If the system is unstable, it may not reach a steady state at all.