2. Transfer Functions [25 points] Consider the following system differential equation: d³y(t) dt d²y(t) dy(t) -7. dt² dt +36- -130y(t) = du(t) dt +5u(t) a) find the Laplace transform of the ODE, assuming zero initial conditions. V(5) b) Find the transfer function for the system, G(s) =) c) Find the poles and zeros of the transfer function. Hint: MATLAB's "roots" function may be helpful in factoring the denominator polynomial. d) Find the Laplace transform for the output, Y(s), if the input is u(t) = cos(6t). Note: It is okay to express you answer as the multiplication of several polynomials; no need to expand.

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