Natural boundary condition also known as additional or dynamic boundary condition, which results from the balance of moments or forces in the boundary. For example in case of a free-free beam which may be a model of a flying aeroplane or a spacecraft, at both the ends in this system shear force and bending moments are zero (Fig. 10.3). Hence they constitute the natural boundary conditions.

In some systems one may find both the geometric and natural boundary conditions. For example in case of a simply supported beam, both deflection and bending moment at end points are zero. Hence the boundary condition in this case may be termed as mixed boundary conditions. Now let us consider specific examples of continuous one-dimensional systems.