In Exercise, show that the given nonlinear functions are linear when plotted on semilogarithmic or logarithmic paper.
If experimental data are plotted on semilogarithmic paper, and the points the on a straight line, it is possible to determine the function (see Exercise 1). The following data come from an experiment designed to determine the relationship between the voltage across an inductor and the time, after the switch is opened. Determine v as a function of t.
v(V) | 40 | 15 | 5.6 | 2.2 | 0.8 |
t (ms) | 0.0 | 20 | 40 | 60 | 80 |
Exercise 1
In Exercise, show that the given nonlinear functions are linear when plotted on semilogarithmic or logarithmic paper.
A function of the form y = a(bx) is a straight line on semilogarithmic paper, since log y = log a + x log b is in the form of a straight line. The variables are log y and x, the slope is log b, and the intercept is a. (To get the slope from the graph, we calculate (log y − log a)/x for some set of values x and y. The intercept is read directly off the graph where x = 0.) Plot y = 3(2x) on semilogarithmic paper to verify this analysis.
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