## 4 Experiments
### Resonance  
The resonance behavior is determined by applying a frequency-discretized driving oscillation \(\theta_{d}\sin\Omega_{i}t,\,i=1,\dots,n_{\mathcal{G}}\) of constant amplitude \(\theta_{d}=20^{\circ}\), see Figure 5.  
Each group \(\mathcal{G}^{\Omega_{i}}\) consists of five periods (this number was empirically chosen), each taken after a transient delay time of 3 s, of the same frequency \(\Omega_{i}\), causing the system to reach a steady state oscillation. The mean value (\(\langle\cdot\rangle\) represents the averaging operator) of the measured forced amplitudes \(\langle\varphi_{m}\rangle_{\mathcal{G}^{\Omega_{i}}}\) over one group \(\mathcal{G}^{\Omega_{i}}\) corresponds to the measured forced amplitude of this driving frequency group. Finally, this value is normalised by the amplitude of the driving oscillation \(\theta_{d}\), which leads to the following amplitude response [27]:  
\[\varphi_{r}^{*}=\frac{\langle\varphi_{m}\rangle_{\mathcal{G}^{\Omega_{i}}}}{ \theta_{d}}\,, \tag{6}\]  
which is used in the following figures. The amplitude response for different pretensions, i.e., the uniform change in length of the tendons, over the frequency (the amplitude response over time can be found in Supplementary Video S1) is plotted in the left graph of Figure 6. The tube shown surrounding each solid average line represents one standard deviation, where \(n_{m}=3\) measurements were taken for each pretension. In this, the effect can be observed that as the pretension increases, the resonance frequency \(f_{r}\) shifts to higher frequencies and the resulting amplitude response \(\varphi_{r}^{*}\) decreases. For a system behaving like a harmonic oscillator with constant natural angular frequency \(\omega_{0}\), a shift of its resonance maximum to smaller frequencies with decreasing amplitude should be observed as [PERSON]'s damping factor \(D\) increases [27]. This discrepancy will be discussed in the next section and possible explanations will be given. The phase difference analysis, which characterises the resonance from another point of view, is shown in the right graph of Figure 6. The resonant behavior arises from the phase shift of \(\frac{\pi}{2}\), since the resulting velocity \(\phi\) is in phase with the external driving force, and thus, the system permanently receives power. This power increase is only limited by the dissipative friction. An alternative approach is to use the Lissajous curves, see Figure 7, in which the phase shift can be shown in a qualitative way. A certain shape corresponds to a certain phase shift. The advantage here is that no numerical difference has to be computed in order to obtain a time difference, from which the phase shift can be calculated. For an amplitude ratio of 1:1, an ascending line from the lower left to the upper right corresponds to a phase shift \(\Delta\varphi=0\), an evolving ellipse along the former line, forms a circle and then an ellipse again towards a line but rotated to the left undergoes the phase shifts \(\Delta\varphi\in[0,\,\pi]\). Technical limits become apparent here, as the driv  
Figure 5: Frequency-discretized driving oscillation of constant amplitude. ing amplitude \(\varphi_{d}\) does not provide the nominal amplitude at high frequencies. Presumably, this would allow for a wider resonance range with a higher amplitude response. A generalised experiment on the sensitivity of the continuum's compression state is depicted in Figure 8. Here, the amplitude response changes over a continuous interval of tendon lengths by iteratively adjusting the length of the four tendons \(p_{i}\) simultaneously. The point of resonance shifts to higher frequencies and the forced amplitude becomes smaller with increased pretension. An additional effect occurs after reaching a certain threshold of the pretension. Here, the normalized amplitude remains bounded to a value of one. This can be understood as a type of saturation and thus defines a usable range in which the resonant behavior of the continuum can be used.