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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
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2
H (t) = 9.25 sin π t − π + 12.55. Below is a graph of our data with the curve y = H (t).
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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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