An infinite rod has an initial square-pulse displacement function \(\eta(0, x)=C\), a constant, for \(|x| \leq b\) and \(\eta(0, x)=0\) for \(|x|>b\).

(a) Find the displacement function \(\eta(t, x)\) at later times, assuming all mass points in the rod are initially at rest.

(b) Carry out a Fourier transform of \(\eta(0, x)\) to determine \(g(0, k)\), which shows the degree to which various wavelengths make up the square pulse.