(Forcced oscillation & Damped oscillation)

The measurement principle of this experiment is based on a standard measurement procedure. Spring oscillator, formed of a spring - stiffness *k* and the mass - weight *m*, is deflected from the equilibrium position. In the case study damped oscillations enough to "swing" system, then stop wake up and watch the vibrations. Damping coefficient δ can be determined from the time recording instantaneous deflection of the quasi-periodic motiont (damped oscillation). In the case that we are investigating the amplitude at the excitation frequency (forced oscillation), we will follow the course of immediate deflection at different excitation frequencies of the exciting force.

Excitation power is generated by a magnetic force for both cases (damped oscillations and forced oscillations). Neodymium magnet is glued to the lower side of weights. Coil with ferromagnetic core is fixed under the vibrating are boiled (see diagram principle - right). The electromagnetic coil is powered by alternating current with variable frequency. It reaches different frequencies of excitation power. The system is still fitted with damping element for the possibility of measuring the damped oscillations. It also serves as a protection against an uncontrolled increase in the amplitude of the resonance.

The coil is powered by a alternating current controllable power-supply for the excitation frequency changes needed by computer. Control signals for the resource, as well as immediate loading deflection oscillator operates experimental kit ISES. This kit has several input and output ports that can connect different experimental modules – voltmeter, amperemeter, the strain gauge… etc. Experimental System ISES is supplemented by a software kit *iSES Web Control*, which is created for using the remote tasks management.

We begin measurements by studying damped oscillation. We choose the situation (by changing the excitation frequency), when the spring oscillates with adequate amplitude. The frequency at the moment given the frequency of the exciting force. The oscillator starts to oscillate with the free oscillations – frequency given by (3) – when we turn off the excitation force (excitation frequency is set to 0 Hz). We enable data recording and monitor the gradual reduction of the maximum deflection of oscillation.

Recorded data can be loaded into any spreadsheet (MS Excel, OO Calc etc.), where the experimental data can be further processed. further. We can deduct the value of the maximum deflection (see Fig. above) that exponentially decreases. You can determine the damping coefficient δ by calculating the exponential regression, which can be done in a spreadsheet.

The other (more complex) option is to let damping factor δ calculate the using a spreadsheet *Solver* extension. Quantifying can be performed from the values of maximum deflections or from across the dependence of immediate displacement. In this case the experimental data except for the immediate displacement calculate the theoretical data from equation (4), wherein the damping coefficient is about a selected parameter.

We use again the Solver (Excel extension) for the best estimate of the damping coefficient. We express the sum of the squared differences of experimental and theoretical values (so-called Squares) – mathematical model designed by equation (4). Solver tool, then enter the task of finding a damping coefficient (or the frequency) to the sum of squared deviations (squares) two series of minimum values. We then enter to the Solver tool the task of finding a damping coefficient (or the frequency) so that the sum of squared deviations (squares) will be minimal. We obtained these parameters mathematical model that will determine what compliance does not improve theoretical measurements and theoretical assumption damped oscillations, after a successful calculation.

We will monitor the amplitude oscillation, depending on the frequency (or angular frequency) of the excitation forces in the stydy of a **forced oscillation** – see equation (5). We'll read maximum deflection or store throughout the immediate displacement, from which we get the amplitude during further processing, at different excitation frequencies. The goal is to get as much data as possible to create a graph of maximum deflection excitation frequency.

We can monitor the this dependence qualitatively directly using a webcam in real experiment. Then we will use experimental data obtained for qualified qualitative estimation. For comparison, our estimates and experimental data can again use a spreadsheet, where the real data can be compared with values obtained from the expression (5) or (6).

**webcam**- the camera follows the real experiment (it is possible to observe the magnitude of the immediate displacement of the spring oscillator)**record experimental data**- experimental data can be saved using the record buttons and later viewed or downloaded to a PC**excitation frequency setting**- excitation frequency can be set to values obtained (buttons) or continuously varied (slider)**graph of instantaneous values**- the instantaneous value of the excitation voltage (red), and the immediate extension of the spring (blue) are plotted in a diagram