I. II. IV. V. 5 s(s+s+2)' Determine whether f(t) is converged or not. VI. Consider the function of F(s) = III. Determine Laplace Transform of f(t) = r(t)e-at. where F(s) is the Laplace transform of f(t). A system dynamics of a linear time invariant continuous system is given by 1 A = [] determine its characteristic equation and comment on the stability issue. The state-variable description of a linear autonomous system x = Ax, where x is a two- dimensional state vector and A is a matrix given by A = 3. Determine the poles of -2 the system. Determine the damping ratio of a system where its characteristic equation is given as s + 2s+8= 0. For each of the following equations, determine the transfer function X (s)/Y(s) and compute the characteristic roots: a. 5x + 7x = f(t) b. 3x + 30x + 63x = 5f(t) c. x + 10x + 21x = 4f(t) d. + 14x + 49x = 7f(t) e. * + 14x + 58x = 6f (t) + 4f(t) f. 5x + 7x = 4f (t) + 15f (t) I. II. IV. V. 5 s(s+s+2)' Determine whether f(t) is converged or not. VI. Consider the function of F(s) = III. Determine Laplace Transform of f(t)=r(t)e-at. where F(s) is the Laplace transform of f(t). A system dynamics of a linear time invariant continuous system is given by 1 A = [] determine its characteristic equation and comment on the stability issue. The state-variable description of a linear autonomous system x = Ax, where x is a two- dimensional state vector and A is a matrix given by A = 3. Determine the poles of -2 the system. Determine the damping ratio of a system where its characteristic equation is given as s + 2s+8 = 0. For each of the following equations, determine the transfer function X (s)/Y(s) and compute the characteristic roots: a. 5x + 7x = f(t) b. 3x + 30x + 63x = 5f(t) c. x + 10x + 21x = 4f(t) d. + 14x + 49x = 7f(t) e. * + 14x + 58x = 6f (t) + 4f(t) f. 5x+7x = 4f (t) + 15f (t)