Consider the following system transfer function,

\[G(s)=\frac{(3 / 2) s+(12 / 8)}{(6 / 4) s^{2}+150 s}\]

(a) Show that the function can be broken into four simple factors: a constant, a zero, a pole, and an integral.

(b) Write down the cut-off frequencies of the zero and pole factors. What is the significance of these frequencies?

(c) Draw the Bode plots of these four factors separately.

(d) Obtain the two overall Bode plots (magnitude and phase angle) for the system.

(e) Derive and draw the Bode plots for a pure time delay function represented by \(f(t-\tau)\).

(f) If the above system has a time delay of one second, how does this affect its Bode plots? Illustrate your answer.