Oscillation frequencies of plant stems with apical loads.

The frequency of free oscillations of plant stems with apical loads, as found in some cereals, is different depending on whether the stems are oriented vertically or horizontally. Neglecting the stem's own weight the differential equations describing the oscillation can be solved for both cases, although in the vertical orientation only for a limited set of conditions including constant bending stiffness along the stem. Comparison with experimental data shows that the difference between the oscillation frequencies in vertical and horizontal orientations can be attributed to the fact that in the vertical orientation the top load due to gravity induces a bending moment varying with the oscillation, while in the horizontal case this bending moment is nearly constant.