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Damped harmonic motion question

  1. Apr 22, 2010 #1
    A damped harmonic motion starts from rest at time t=0 with displacement A0 has the equation:

    x(t) = A0/cos (delta)*e^(-t/tau) *cos (w't + delta)

    w' is the angular frequency, tau is the time constant and delta is given by:

    tan (delta) = - (1/w' tau)

    find the time when the maximum negative displacement occurs. express it in terms of period.



    So, Can you just give me a hint on where to start and where to go from there.

    Thank you
     
  2. jcsd
  3. Apr 22, 2010 #2

    kuruman

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    Hint: Which term in your expression for x(t) can conceivably turn negative as time increases? Is it the exponential or is it the cosine?
     
  4. Apr 22, 2010 #3
    That would be the exponential since we have -t in there. So i guess in this case i am supposed to differentiate with respect to t first?
     
  5. Apr 22, 2010 #4

    kuruman

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    Just wait before you take any derivatives.

    [tex]e^{-t}=\frac{1}{e^t}[/tex]

    For what value of t is the expression negative?
     
  6. Apr 22, 2010 #5
    oh oops i dint see that part. The exponential is going to give me a positive value. How did i forget that. my bad
     
  7. Apr 22, 2010 #6

    kuruman

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    Do you know where to go from here? The first thing to do is to find a value for the phase delta.
     
  8. Apr 22, 2010 #7
    I dont know exactly where to go since i am confused about what it is asking for exactly. And to find the value for delta i will be using the tan (delta) = (1/w' tau) and then i guess i can substitute w' = 2*pi/ T' in there and go from there?
     
  9. Apr 22, 2010 #8

    kuruman

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    You are given x(t) and you are told that at t = 0, the oscillator is at A0. If you evaluate your expression at t = 0, i.e. find x(0), is it equal to A0 or is it equal to something else?
     
  10. Apr 22, 2010 #9
    ohhh i see.. no problemo.. thank you
     
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