6 r cos 32 r sin2 9 r2 cos2 6r cos 9 r2

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Unformatted text preview: r to 12.55 than the next value, φ 15.9, which corresponds to t = 4. Hence, − ω = 3, so φ = −3ω = −3 π = − π . We have 6 2 H (t) = 9.25 sin π t − π + 12.55. Below is a graph of our data with the curve y = H (t). 6 2 2. Using the ‘SinReg’ command, we graph the calculator’s regression below. While both models seem to be reasonable fits to the data, the calculator model is possibly the better fit. The calculator does not give us an r2 value like it did for linear regressions in Section 2.5, nor does it give us an R2 value like it did for quadratic, cubic and quartic regressions as in Section 3.1. The reason for this, much like the reason for the absence of R2 for the logistic model in Section 6.5, is beyond the scope of this course. We’ll just have to use our own good judgment when choosing the best sinusoid model. 11.1.1 Harmonic Motion One of the major applications of sinusoids in Science and Engineering is the study of harmonic motion. The equations for harmon...
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