Physics-informed machine learning is a methodology that combines principles from physics with machine learning techniques to enhance the accuracy and interpretability of predictive models. By incorporating physical laws and constraints into the learning process, physics-informed machine learning enables more robust predictions and reduces the need for large amounts of training data. In part II of this two-part series, the authors present structural response forecasting using a physics-constrained methodology to solve the homogeneous second-order differential equations that constitute the equation of motion of a linear structural system. This forward problem is formulated to allow the incorporation of numerical methods into the training process while using segmented training to circumvent intrinsic stability limitations to the physics-informed machine learning problem. The ability of physics-informed machine learning to make generalizations for limited training data is discussed.