Vibration suppression is an important capability for collaborative robots deployed in challenging environments such as construction sites. We study the active suppression of vibration caused by external sources such as power tools. We adopt the band-limited multiple Fourier linear combiner (BMFLC) algorithm to learn the vibration online and counter it by feedforward force control. We propose the damped BMFLC method, extending BMFLC with a novel adaptive step-size approach that improves the convergence time and noise resistance. Our logistic function-based damping mechanism reduces the effect of noise and enables larger learning rates. We evaluate our method on extensive simulation experiments with realistic time-varying multi-frequency vibration and real-world physical interaction experiments. The simulation experiments show that our method improves the suppression rate in comparison to the original BMFLC and its recursive least squares and Kalman filter-based extensions. Furthermore, our method is far more efficient than the latter two. We further validate the effectiveness of our method in real-world polishing experiments. A supplementary video is available at https://youtu.be/ms6m-6JyVAI.