## 2 Materials and Methods
### Calibration Function of the Frequency Response  
According to DIN ISO/IEC 17025 testing and calibration laboratories must make sure that their \"Measuring equipment shall be calibrated when the measurement accuracy or measurement uncertainty affects the validity of the reported results\" [28]. When investigating elements with stiffness, damping and mass properties, the phase shift between the excitation signal and force signal is essential. The phase shift shows which mechanical property is involved and thus makes the characterization of the element possible. The validation of non-standardized or modified test methods must meet the requirements of the specific application. \"Calibration or evaluation of bias and precision using reference standards or reference materials\" [28] is a typical procedure when calibrating. A calibration weight is used as a reference standard for static calibration since it is directly related to the acceleration of gravity and physical quantity. For dynamic calibration, the time must be taken into account, as well as the disturbance variables over time. Systematic disturbances can result from the sensor and measurement delay, from the moving mass of the test system itself, or electronic, computational and numerical factors at the sensor, transducer, cables and acquisition system. [PERSON] et al. [25] demonstrate the use of this method for biodynamic responses of human hand-arm models. They report that few researchers provide detailed information on their instrumentation characteristics, systematic evaluations and dynamic calibrations. They expect that a large part of the deviations of dynamic responses in literature is due to a lack of mass cancellation. Their demonstrated mass cancellation is based on the electronic compensation of [PERSON] [27], who points the first idea of mass cancellation back to [PERSON] [26]. [PERSON] et al. [29] successfully apply mass cancellation (building on the uncoupling techniques in structural dynamics [30; 31]) for a complete FRF matrix to a simple numerical example. [PERSON] [26] states, that there are two possible calibrations of test systems in the field of modal analysis. First, the absolute calibration of all independent individual measured variables. In practice, this is only possible for individual sensors under strictly controlled conditions. Second, [PERSON] [26] presents the possibility of calibrating systems using the ratio of two variables whose combination can be measured accurately. He proposes to measure the ratio of acceleration \(\ddot{x}\) and force \(F\), which is the inverse of AM for a known mass \(m\), a quantity that can be accurately determined by weighing [26]. To measure the test object, the moving mass belonging to the test setup must be subtracted. As shown in Figure 1b the total measured mass \(m_{meas. }\) is separated into the moving mass of the test setup \(m_{sensor}\) and \(m_{testobj.}\). Assuming that, the added mass \(m_{sensor}\) behaves similar to a rigid body, we can conclude that the force actually applied to the test object differs from the measured force by the mass \(m_{sensor}\) times the acceleration \(\ddot{x}(\omega)\) and effects the real part of the measurement of \(AM_{testobj.}(\omega)\). \[F_{testobj.}(\omega)=F_{meas.}(\omega)-m_{sensor}\cdot\ddot{x}(\omega) \tag{6}\]  
\[AM_{testobj.}(\omega)=\frac{F_{testobj.}(\omega)}{\ddot{x}(\omega)}=\frac{ F_{meas.}(\omega)}{\ddot{x}(\omega)}-m_{sensor} \tag{7}\]  
\[Re(AM_{testobj.}(\omega))=Re(AM_{meas.}(\omega))-m_{sensor} \tag{8}\]  
\[Im(AM_{testobj.}(\omega))=Im(AM_{meas.}(\omega)) \tag{9}\]  
[PERSON] [27] formulates an error term that changes in magnitude and phase over frequency. To correct this error, he formulates the _measurement systems FRF_\(HI_{pp}\). That represents the overall system characteristic, including electrical and mechanical behavior (see Ref. [27] for more details). \[AC_{testobj.}(\omega)=\frac{AC_{meas.}(\omega)}{HI_{pp}(\omega)-m_{sensor} \cdot AC_{meas.}(\omega)} \tag{10}\]  
\(AC_{meas.