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1) The signal x, it) is pestodfc ustth pertod T.=2. Thus at 2 -- dt + at -Tant 270 (- cos(an) %3D 2777 usten n=0 then xvo= actt %3D + 2 cosckn) cas(ant) Thus and x,(t)=1. It folboos then that L2,n=0, +nt0

1) The signal x, it) is pestodfc ustth pertod T.=2. Thus at 2 -- dt + at -Tant 270 (- cos(an) %3D 2777 usten n=0 then xvo= actt %3D + 2 cosckn) cas(ant) Thus and x,(t)=1. It folboos then that L2,n=0, +nt0

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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In the image that I have attached, I have some questions about numbers 1 and 2. For number 1, how is the integral from -1 to 1 like in the formula, its -a/2 to a/2 so why did a =2 or is this not correct. Also for number 2, why does x_2(t) =1 and what does it mean, "It follows then that x_2,0 = 1 and x_2,n = 0, ∀n = 0.

) The signal x,lt) is pestodfe ustth pertad T.=2. fant dt Thus dt + at t e te ((- cos(an) 27377 ushen n=0 then xo= actdt 1- +2E (- coscn) cas(ant) Thus ,(E) = x, (t)=1. It folbos then that and 2,n=0, + n+o 3 The sigral is perfodie wofth pexfed To= 1. To ts'ete-faont ot = jef m Thus To -ban + 1 4) The signal ct) is pexiodic with pertod T, = 27 ashereas cos (2:5) is pestodic otth pesiod T, = 0.87. IH ollows that casct)+ coek.st5 is pesfodic oith pestod T= The trigonometsic Fouriex sexies the even cos (t)+ Ces (2-st) => T= 2T, =ST, = YT %3D Tz 087 sfgral co (t)+ Ces(2st) is - d, cas (2) - ncos(3t) DEI Ey oqualiny the cofficlents a cas) bath sides we dseve that an =0 fo8 all n unleas n= 2,5 o uohieh cose a=ag=| Hence xy,2 = s = fox n= 2,5 and yn= 0 fo8 all othes values of
Transcribed Image Text:) The signal x,lt) is pestodfe ustth pertad T.=2. fant dt Thus dt + at t e te ((- cos(an) 27377 ushen n=0 then xo= actdt 1- +2E (- coscn) cas(ant) Thus ,(E) = x, (t)=1. It folbos then that and 2,n=0, + n+o 3 The sigral is perfodie wofth pexfed To= 1. To ts'ete-faont ot = jef m Thus To -ban + 1 4) The signal ct) is pexiodic with pertod T, = 27 ashereas cos (2:5) is pestodic otth pesiod T, = 0.87. IH ollows that casct)+ coek.st5 is pesfodic oith pestod T= The trigonometsic Fouriex sexies the even cos (t)+ Ces (2-st) => T= 2T, =ST, = YT %3D Tz 087 sfgral co (t)+ Ces(2st) is - d, cas (2) - ncos(3t) DEI Ey oqualiny the cofficlents a cas) bath sides we dseve that an =0 fo8 all n unleas n= 2,5 o uohieh cose a=ag=| Hence xy,2 = s = fox n= 2,5 and yn= 0 fo8 all othes values of
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