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[Computer] Find the Fourier coefficients an and bn for the
Chapter 5, Problem 5.49(choose chapter or problem)
[Computer] Find the Fourier coefficients \(a_{n}\) and \(b_{n}\) for the function shown in Figure 5.28(a). Make a plot similar to Figure 5.23, comparing the function itself with the first couple of terms in the Fourier series, and another for the first six or so terms. Take \(f_{\max }=1\).
Figure 5.28 (a) Problem 5.49. (b) Problem 5.50
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QUESTION:
[Computer] Find the Fourier coefficients \(a_{n}\) and \(b_{n}\) for the function shown in Figure 5.28(a). Make a plot similar to Figure 5.23, comparing the function itself with the first couple of terms in the Fourier series, and another for the first six or so terms. Take \(f_{\max }=1\).
Figure 5.28 (a) Problem 5.49. (b) Problem 5.50
ANSWER:Step 1 of 4
The given function is even, \(f(-t)=+f(t)\). Therefore, \(\sin (m \omega t) f(t)\) is odd and all of the integrals (5.84) for the coefficients \(b_{m}\) are zero. Since \(\cos (m \omega t) f(t)\) is even, the coefficients \(a_{m}\), are not necessarily zero. Bearing in mind that \(\tau=2\), so \(\omega=\pi\), we find that
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Review this written solution for 102065) viewed: 527 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 5 - Problem 5.49
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