Consider the transfer function:
G(s)=\frac{0.7\left(s^{2}+2 s+2\right)}{s^{5}+5 s^{4}+2 s^{3}+4 s^{2}+6}
(a) Plot its poles and zeros in the complex plane. A computer program that calculates the roots of the polynomial (such as the command roots in MATLAB) can help you factor the denominator polynomial.
(b) From the pole locations in the complex plane, what can be concluded about the output modes for any input change?
(c) Plot the response of the output to a unit step input. Does the form of your response agree with your analysis for part (b)? Explain.
