1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simple Harmonic Oscillator

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that the underdamped oscillator solution can be expressed as x(t)=x[itex]_{0}[/itex]e[itex]^{-γt}[/itex][cos(Ω't+((v[itex]_{o}[/itex]+γx[itex]_{o}[/itex])/(x[itex]_{o}[/itex]Ω')sinΩ't] and demonstrate by direct calculation that x(0)=x[itex]_{o}[/itex] and [itex]\dot{x}[/itex](0)=v[itex]_{o}[/itex]
    2. Relevant equations

    The underdamped oscillator solution is

    3. The attempt at a solution
    This problem completely overwhelms me so my solution may be a little lacking...
    I took the general form
    A=acos([itex]\alpha[/itex]) and B=-asin([itex]\alpha[/itex])
    Which according to what I read in the book should yield
    So im thinking that the equation ae[itex]^{-γt}[/itex]cos(Ω't+[itex]\alpha[/itex]) can be transformed into a more useful form using the same method

    and that is sadly as close as I could get

    Any input would be appreciated. Thanks.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 24, 2012 #2
    You wrote,


    I think you are missing some ")" somewhere?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook