A rod of length \(L\) is clamped at both ends \(x=0, L\) so that the displacement function obeys \(\eta(t, 0)=\eta(t, L)=0\). Initially the displacement function is \(\eta(0, x)=\) \(b \sin ^{2}(\pi x / L)\) and \(\partial \eta(t, x) /\left.\partial t\right|_{0}=0\), where \(b\) is a positive constant. Find a Fourier-series representation of the solution of the wave equation at all future times.