I took data using the motion detector viewing a large pan supported by a spring. The large area of the pan assures good damping. The pan was viewed from below and the data were imported into IGOR for plotting purposes and curve fitting.
The first plot shows the displacement vs time. The data (red points) were fit to a damped sine wave. The fit is shown in blue and the fit results from IGOR:
x[t] = 0.6 + 0.07*exp[-0.06t]*sin[4.41*t + 5.0]
The green plot just shows the exponential part.
The next plot shows the displacement (in red) and the velocity (in blue). Note that they are out of phase by 90o. There are data plotted.
Finally the last plot shows the displacement (in red) and the acceleration (in green). Note that they are out of phase by 180o.
