A dynamic system is described by the following State-Variable Matrix model such that: \(\dot{\mathbf{x}}=\mathbf{A x}\) and \(\mathbf{y}=\mathbf{C x}\), where

(a) Obtain the State-Transition Matrix \(\Phi(\mathbf{t})\).

(b) Find the state variable responses \(x_{1}(t)\) and \(x_{2}(t)\).

(c) Find the output response \(y(t)\).

(d) For this system verify that

Transcribed Image Text:

0 1 - A= C=3 -1] 0 -2 and x(0) = [12].