Final answer:
The transfer function G(s) = (5s+11)/(s^2+5s+6) represents a dynamic system with input f and output y. To find the output y as a function of the input f, you can use the inverse Laplace transform and perform partial fraction decomposition. The result will give you the time-domain representation of the system.
Step-by-step explanation:
The transfer function G(s) = (5s+11)/(s^2+5s+6) represents a dynamic system (ODE) with input f and output y. The transfer function describes the relationship between the input and output of the system in the Laplace domain. To find the output y as a function of the input f, you can use the inverse Laplace transform. In this case, the inverse Laplace transform of G(s) can be found using partial fraction decomposition.
To perform partial fraction decomposition, factor the denominator of G(s) as (s+2)(s+3). Then, you can express G(s) as A/(s+2) + B/(s+3), where A and B are constants. By equating the numerators, you can solve for the values of A and B. Once you find the partial fraction decomposition, you can apply the inverse Laplace transform to each term to find the time-domain representation of the system.
For example, if f(t) = e^(-2t), you can use the inverse Laplace transform to find y(t) in terms of e^(-2t). This will give you the response of the system to the given input.