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Simple Harmonic Motion

  1. Nov 27, 2007 #1
    1. The problem statement, all variables and given/known data
    (a) Show that A[tex]_{0}[/tex]cos([tex]\omega[/tex]t+[tex]\delta[/tex]) can be written as A[tex]_{s}[/tex]sin([tex]\omega[/tex]t)+A[tex]_{c}[/tex]cos([tex]\omega[/tex]t), and determine A[tex]_{s}[/tex] and A[tex]_{c}[/tex] in terms of A[tex]_{0}[/tex] and [tex]\delta[/tex].
    (b) Relate A[tex]_{c}[/tex] and A[tex]_{s}[/tex] to the initial position and velocity of a particle undergoing simple harmonic motion.




    2. Relevant equations
    x=Acos([tex]\omega[/tex]t+[tex]\delta[/tex])
    v[tex]_{x}[/tex]=-[tex]\omega[/tex]Asin([tex]\omega[/tex]t+[tex]\delta[/tex])




    3. The attempt at a solution
    I have absolutely no idea where to begin...please help!!! Thanks a bunch for whoever does!

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 27, 2007 #2

    Astronuc

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    Staff: Mentor

    Start with the trigonometric identity for cosine of the sum of two angles, e.g. cos (a+b) = cos a cos b - sin a sin b, and see where that leads.

    The initial position and velocity are taken at t = t0 or t = 0?
     
  4. Dec 4, 2007 #3
    I got the first part by using the trig identity and then taking the derivative, except I don't know why I had to take the derivative but it worked out anyway so I did.
    Now, if t=0 then that would make the sine portion of the position 0 and the cosine portion 1 so the initial position would equal Ac, right?
    For velocity, what would I do with that or is my whole idea wrong?
     
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