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Cant understand from where the numbers come from

  1. Jun 26, 2009 #1
    suppose that the nonlinear resistor R has a characteristics specified by the equation:
    [tex]
    v=20i+i^2+0.5i^3
    [/tex]
    express v as a sum of sinusoids for
    [tex]
    i(t)=cos \omega _1t +2cos \omega _2t \\
    [/tex]
    the solution in the book is
    http://i43.tinypic.com/eve807.gif

    i get a differnt expression why??
    [tex]
    v=20cos \omega _1t +40cos \omega _2t + cos^2 \omega _1t +4cos (\omega _1t) cos (\omega _2t)+4cos^2 \omega _2t+0.5cos^3 \omega _1t+2cos^2 \omega _1tcos \omega _2t+0.5cos^3 \omega _1t+2cos \omega _1tcos^2 \omega _2t+4cos^3 \omega _2t
    [/tex]
     
  2. jcsd
  3. Jun 26, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You haven't completely reduced. For example, you have powers and products of cosines. Those can be reduced to first power by trig identitities: [itex]cos^2(\omega_1t)= (1/2)(1+ cos(2\omega_1t))[/itex] and [itex]cos(\omega_1t)cos(\omega_2t)= (1/2)(cos((\omega_1+\omega_2)t)+ cos((\omega_1- \omega_2)t))[/itex].
    [itex]cos^3(\omega_1t)[/itex] can be written as [itex]cos(\omega_1t)cos^2(\omega_1t)= cos(\omega_1t)(1/2)(1+ cos(2\omega_1t))[/itex] which can be reduced, and so on.
     
  4. Jun 26, 2009 #3
    still i cant see i get numbers here
    like they did
    as far is i know only sin^2 a +cos^2 a =1

    and my expression and not your has anything near that
     
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