This paper shows analytical and experimental evidence of using the vibration dynamics of a compliant whisker for accurate terrain classification during steady state motion of a mobile robot. A Hall effect sensor was used to measure whisker vibrations due to perturbations from the ground. Analytical results predict that the whisker vibrations will have a dominant frequency at the vertical ... [Show full abstract] perturbation frequency of the mobile robot sandwiched by two other less dominant but distinct frequency components. These frequency components may come from bifurcation of vibration frequency due to nonlinear interaction dynamics at steady state. Experimental results also exhibit distinct dominant frequency components unique to the speed of the robot and the terrain roughness. This nonlinear dynamic feature is used in a deep multi-layer perceptron neural network to classify terrains. We achieved 85.6\% prediction success rate for seven flat terrain surfaces with different textures.