Consider the transfer function (G(s) = fracs²/(s - 1)(s - 2)). Find (z) such that the steady-state response (y) equals zero for the input (u(t) = cos (ω₀ t - 4)). Plot in MATLAB (|G(jω)|) for (ω₀ = 3).
a) Determine the value of (z) satisfying the given condition.
b) Analyze the impact of (z) on the steady-state response.
c) Plot (|G(jω)|) in MATLAB for the specified (ω₀).
d) Evaluate the significance of the cosine term in the input.