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8 Odd Half - Range Extension Create the odd function go(t) by flipping fo(t) 180° around the vertical axis and then the 180° around the horizontal axis. Left half of go(t) is shown below. Carefully draw the left half to scale on the right diagram below. go (t) fo (t) 0 +1 Then Create the periodic function g(t) with period 8 NEXT Find expression for coefficients n sin bn. Show that bn has the form: bn To obtain sin COS COS TTTT 4 nπ Add lines to the left side to COMPLETE plot for go(t) plot 4 Сп Dn +4 Cn Dn n n² values for Cn and Dn. Show they repeat. 2 3 5 1 4 = + 8. 6 . Fill the following Table +1 7 8 +4 t

8 Odd Half - Range Extension Create the odd function go(t) by flipping fo(t) 180° around the vertical axis and then the 180° around the horizontal axis. Left half of go(t) is shown below. Carefully draw the left half to scale on the right diagram below. go (t) fo (t) 0 +1 Then Create the periodic function g(t) with period 8 NEXT Find expression for coefficients n sin bn. Show that bn has the form: bn To obtain sin COS COS TTTT 4 nπ Add lines to the left side to COMPLETE plot for go(t) plot 4 Сп Dn +4 Cn Dn n n² values for Cn and Dn. Show they repeat. 2 3 5 1 4 = + 8. 6 . Fill the following Table +1 7 8 +4 t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Odd Half - Range Extension Create the odd function go(t) by flipping fo(t) 180° around the vertical axis and then the 180° around the horizontal axis. Left half of go(t) is shown below. Carefully draw the left half to scale on the right diagram below. fo (t) go (t) 8 0 +1 Then Create the periodic function g(t) with period 8 NEXT Find expression for coefficients Cn. Dn n n² To obtain values for Cn and Dn. Show they repeat. 2 3 5 n bn. Show that bn has the form: bn sin sin COS COS TTTT Add lines to the left side to COMPLETE plot for go(t) plot 4 4 +4 Сп Dn 1 4 = + 8. 6 . Fill the following Table +1 7 8 +4 t
Transcribed Image Text:Odd Half - Range Extension Create the odd function go(t) by flipping fo(t) 180° around the vertical axis and then the 180° around the horizontal axis. Left half of go(t) is shown below. Carefully draw the left half to scale on the right diagram below. fo (t) go (t) 8 0 +1 Then Create the periodic function g(t) with period 8 NEXT Find expression for coefficients Cn. Dn n n² To obtain values for Cn and Dn. Show they repeat. 2 3 5 n bn. Show that bn has the form: bn sin sin COS COS TTTT Add lines to the left side to COMPLETE plot for go(t) plot 4 4 +4 Сп Dn 1 4 = + 8. 6 . Fill the following Table +1 7 8 +4 t
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