Figure 8.

Total energy in the system (scaled). Three cases are presented: forcing only with $\beta =0$, and $\alpha \to \infty$ (i.e. $\alpha =-1$) shown as the solid line, only wall damping ($\beta =0$), shown as the dash-dot line and the dash-line presents the case of wall damping and internal damping ($\beta =5\times {10}^{-5}$). (a) When $\alpha =2.5$, wall damping is the primary method of energy dissipation. (b) Much less energy is dissipated by the dynamic boundary when $\alpha =25$.