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Homework Help: Trigonometric identity forced oscillations

  1. Apr 22, 2007 #1
    1. The problem statement, all variables and given/known data
    http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf [Broken]

    http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf [Broken]

    Question A- (b)

    They use some trigomentric identity that I don't understand, which one is it?

    Thanks in advance.

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Apr 22, 2007 #2


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    Staff Emeritus
    Science Advisor

    Well, you've got an expression that's in the form sinAsinB; so you look to use the formula cos(A-B)=cosAcosB+sinAsinB.

    From this, you know that [tex]\cos\{\omega_it-\phi-\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)+\sin\{\omega_i t-\phi\}\sin(\omega t)[/tex]. You can work out the similar expression that [tex]\cos\{\omega_it-\phi+\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)-\sin\{\omega_i t-\phi\}\sin(\omega t)[/tex] Then subtract the second from the first.
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