Forced vibrations, resonance and damping.

Results:

RA, which controls the amplitude of the oscillations, was set to 97.7 KΩ, which is measured using a multimeter.

For 20 oscillations to occur it took 42.14 seconds.

Therefore, for one oscillation it takes:

42.14 / 20     =     2.107 seconds

So, frequency = 1 / Time period (T)

                 = 1 / 2.107

                 = 0.4746084480

                 = 0.475 (3 sf)

Below is the results table for this experiment:

From the above results table we can see that as the frequency increases so does the amplitude. However as it reaches its natural frequency the amplitude reaches its peak and after its natural frequency the amplitude begins to decrease again. Firstly, for the 3000Ω the amplitude keeps on increasing until the frequency reaches 0.54Hz the amplitude is at its highest of 7.45 cm and after this it begins to decrease again.

The same happens for 500Ω and 1000Ω but for 100Ω the amplitude continues to decrease as frequency is increased.

From Graph One, which shows the results on the same axis we can see many things. Firstly, the graph shows the amplitude against frequency for all of the measurements. The first amplitude for the graph with 3000Ω shows that as the frequency increases the amplitude increases, however after it reaches its peak frequency (around 0.5Hz as worked out earlier) the amplitude begins to decrease. This is the reason for the graph, which rises and the then curves back down like a parabola. For the graph with 1000Ω and 500Ω the same rule applies, however, with these graphs the height to which the amplitude gets to is lower. For example, for 1000Ω the highest amplitude was 3.60 and for 500Ω its only 2.10 cm.

        Another factor/point we can see from the table of results and the graph is for the amplitude, which we used 100 ohms. These results were generally a decline and there was no relationship for this line like the others. The graph shows the straight line achieved by this.

        Therefore, as the amount of resistance decreases from 3000Ω the electromagnetic damping of the galvanometer coil increases. Throughout the experiment we forced the oscillation using the equipment and this allowed us to see when resonance occurs. Furthermore, the amplitude at resonance depends on the amount of damping in the system, which we changed through the experiment. The amount of damping we used during the experiment was controlled by means of a variable resistor connected in parallel with it.