{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "# 4. Graphing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graphing your data shows relationships much more clearly and quickly than presenting the same information in a table. A picture is worth a thousand words, so a well-made graph can save a lot of writing when you report your results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.1 Rough Graphs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rough graphs are made for your own benefit. They don't need to be as polished as graphs that will appear in a report, so they can hand-drawn. Graphing each point as you take it is not a good idea, because that is inefficient. It can prejudice you about the value of the next data point. So take a set data points and then graph them all. \n", "\n", "It is very useful to make rough graphs during lab when you have the chance to do something about any problems. You'll know if you need to check any data point, since any strange measurement will stand out in a graph. You'll also be able to spot regions where you should take more data. Typically, people take approximately evenly spaced data points over the entire range of the controllable (or “independent”) variable, which is certainly a good way to start. A graph of that inital data will tell you if there are regions where you should look more closely: regions where your graph is changing rapidly, going through a minimum or maximum, or changing curvature, for example. The graph helps you identify interesting sections where you should get more data, and saves you from taking lots of data in regions where little is happening. \n", "\n", "For example, Figure 4.1 below shows the initial data taken for a phenomenon called mechanical resonance. All you need to know about resonance is that the amplitude (a measure of the response of an oscillating system) depends on the frequency of oscillating force driving the system. Notice that the driving frequencies were approximately evenly spaced. For the apparatus used, the highest and lowest frequencies attainable were easy to find, and the experimenter chose to space the frequencies evenly to get roughly 10 different frequencies between the extremes. From the graph of the initial data, you can see that the response doesn't change very much at either very high or very low frequencies, but something interesting happens near 5 cycles/s. \n", " \n", "