Data density Suppose you are taking data in an experiment in which you control one variable and measure the effects on another variable. You choose several values of the control variable to use. Are the values that you choose random? Do you choose equally spaced values? Do you take data at a lot of closely spaced values until you get bored, and then switch to wider spacing? The spacing between the values of the control variable that you choose can be called the data density. In some experiments, using an appropriate data density is essential to getting quality results. The data in Fig. 1 is for an experiment to measure the resonant frequency of an oscillator, such as in Experiment #38. Remember that the resonant frequency is the frequency at which the driven oscillator will have the largest amplitude. 1. Graph the data in Fig. 1. Is this enough data to get a good measurement of the resonant frequency?

Driving frequency (Hz) Amplitude (cm) 1.37 2.41 10.14 4.60 1.87 1.18 0.86 0.68 0.56 0.47 0.41 12 0.36 13 0.33 14 0.30 15 0.27 Figure 1: Data set I for resonance experimentDriving frequency (Hz) Amplitude (cm) 1.37 2.41 2.5 3.89 10.14 3.20 28.23 3.22 34.37 3.24 43.92 3.26 60.80 3.27 75.27 3.28 98.78 3.29 143.59 3.30 262.61 3.31 1414.21 3.32 392.23 3.33 175.41 3.34 112.87 3.35 83.19 3.37 54.51 3.39 40.54 3.41 32.27 3,50 16.82 4.596 1.87 1,176 Figure 2: Data set II for resonance experiment