(10 pts) 4. Consider an input signal ft) as shown in the following plot: f(t) f 0 2 *N *t -1 -3 Derive the Laplace transform of f(). (20 pts) 5. The dynamics of a process can be described using the following equation: dT dt 2T - 100F where T is the output and F is the input. The above model has a steady-state with the steady-state input value F. = 2. (10 pts) (a) Derive the linearized model around the steady-state. (10 pts) (b) If the input reduces from F= 2 to F=1 at t = 0, what is the response of T