In: Advanced Math
D^2 (D + 1)y(t)= (D^2 +2)f(t)
a.) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes of the system.
b.) Find y_o(t), the zero-input component of response y(t) for t>=0, if the the initial conditions are y_0 (0) = 4, y_0' (0) = 3, and y_0'' (0) = -1