In this chapter we will continue with applications of Newtonian mechanics for central forces, where the potential U only depends on the magnitude of the relative distance \(|{\vec r}_1-{\vec r}_2|\) between two mass points. In this case the conservation of momentum, angular momentum and energy holds, which drastically reduces the number of free degrees of freedom. An important case are \(1/r^2\) -forces, which holds for Coulomb and gravitational forces; we will classify the trajectories according to their energy and derive Kepler’s laws for the motion of planets. In extension the law of gravity will be derived and gravity fields are introduced for static mass distributions. In addition the dynamics of a linear oscillator is discussed—another important physical system—and the solutions are calculated from the equations of motion also in case of additional frictional forces. The case of a damped oscillator, that is driven by an external periodic force, will lead to the formation of resonances that are analysed in some detail. In addition the problem of coupled harmonic oscillations is addressed, which is characteristic for the vibrational modes in crystals.