## 2 Materials and Methods  
### Biomechanics  
We measured the force applied to a stem, the half-height of the stem (where the force was applied), the angle of the stem, and the time point of each force measurement (i.e., one measurement per milli second) using the Stalker push force meter [9]. Calculations from these data gave the line segment length of displacement of the panicle (the top of the stem), the radius of the line segment (from twice the half-height), the energy applied (and returned), and the power applied in the bending. Please note that E in this paper will represent energy in Joules instead of the Young's modulus. As seen in Figure 1, the angle of the push force meter (and thence the stem) is increased, then decreased. In doing this at a relatively constant rate (holding \(\omega\), the angular velocity, as constant), the force applied to bend a stem, or set of stems, will be uniform and continuous. Mathematically,there is an inflection point at max, meaning that it is not a continuous function, and therefore not strictly differentiable. Figure 1 is similar to the force curve, seen in Figure 2a, which also shows an inflection point at Fmax, which is isochronous with max. The fact that F(\(\theta\)) of the entire series would not pass the vertical line test, and would hence not be a function, necessitates the separation of the two paths as in Figure 2b into bending and unbending. The bending of a given stem deposits an amount of energy into the pivot point around which it is being bent, as in Figure 3. If this energy is to be calculated, the total path length of the bend (\(\ell\)) is needed and may be calculated from the angle and the half-height (h) of the stem, as seen in Figure 3.  
Figure 1: Graphical representation of the angle (\(\theta\)) as a function of time in seconds, as it is recorded in the data logs. Figure 3: An illustration of the bending of a stem of length \(r\) to create a line segment of length \(\ell\). The half-height, where the measuring device contacts the stem, is a distance \(h\) above the ground, and the final angle of bending is denoted as \(\theta\). Figure 2: **(a)** Force as a function of time, as it is recorded in the data logs; **(b)** Force vs. angle. \(F(\theta)\) is not a complete function, therefore it must be decomposed into two functions: the bending function and unbending function. The path length can be seen in Figure 4 as the independent variable, while the force is the dependent variable. Each of the two functions can be integrated to determine the amount of deposited energy (in the bending curve) and the amount of returned energy (in the unbending curve). The energy differential (\(\Delta\)E), or the difference between the two integrals, gives the stored potential energy that stays in the stem. In this system, the length of the line segment is used instead of the total arc length because the plants in question do not always bend in a circular path [4]. The energy is measured as the displacement along this line segment as it lengthens to its end (bending to around 45\({}^{\circ}\)) and as it returns to vertical (unbending). To calculate the total energy difference between bending and unbending, the energy of both bending and unbending must first be calculated as:  
\[E_{bending}=\int\limits_{\text{O}}^{\ell max}F_{bending}(\ell)d\ell=\int \limits_{\text{O}}^{\theta max}F_{bending}(2h\ \cos(\theta))d\theta \tag{1}\]  
\[E_{unbending}=\int\limits_{\text{O}}^{\ell max}F_{unbending}(\ell)d\ell=\int \limits_{\text{O}}^{\theta max}F_{unbending}(2h\ \cos(\theta))d\theta \tag{2}\]  
where \(\ell_{max}\) is the maximum displacement in the line segment, \(\ell\) is the line segment displacement, \(h\) is the half-height of the stem, is the angle, \(\theta_{max}\) is the ultimate angle of the bend, \(F_{bending}\) and \(F_{unbending}\) are the bending and unbending force data in N, respectively, and \(E_{bending}\) and \(E_{unbending}\) are the bending and unbending energies in J, respectively.