This work investigates the spectral behaviour and resonance mitigation in a rectangular channel of length \(L\) and width \(d\) with a localized rectangular bottom perturbation. Starting from the two-dimensional wave equation with Neumann boundary conditions, the stationary problem is first formulated and the eigenfrequencies \(\xi _{n,m}\) are obtained by separation of variables for the flat-bottom case. An explicit second-order finite-difference scheme is then implemented to discretise the dynamical system and, through numerical simulations, to explore the appearance of trapped modes and amplitude peaks when the excitation frequency \(\xi \) approaches the threshold \(\xi _1\) . The results confirm the presence of a resonant mode \(\omega \) distinct from \(\xi _1\) under certain geometric symmetry conditions of the bottom perturbation. Finally, a velocity-feedback control strategy is proposed by adding a dissipative term proportional to \(\partial \phi /\partial t\) at an actuator point. Numerical experiments show that this control approach reduces the main resonance peak amplitude from 13.4 to 10.3, achieving a \(23.1\%\) attenuation, while also suppressing a secondary trapped mode, confirming the robustness of the strategy.