Final answer:
The steady-state error of the unity feedback system cannot be calculated because the system is unstable.
Step-by-step explanation:
The steady-state error of a system can be found by evaluating the input function at the output of the system when it has reached a steady-state. In this case, the input function is 8t²u(t), which is a polynomial multiplied by the unit step function. The system transfer function G(s) represents the system's response to an input in the Laplace domain.
To find the steady-state error, we need to find the final value of the system's output. This can be done by finding the system's steady-state gain, which is the value of G(s) when s=0. Evaluating G(s) at s=0, we get:
G(0) = 375(5)(18)(54)/(0)(8)(24) = 590625/0
Since the denominator is zero, the system is unstable and does not reach a steady-state. Therefore, the steady-state error cannot be calculated for this system.