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Damped oscillation equation

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data
    The equation for a damped oscillation is [tex]y(t)=Ae^{-\frac{b}{2m}t}cos(\omega't + \phi)
    [/tex]
    We know that y(0)=0.5 and y'(0)=0.

    Find the values of A and ø and then plot the oscillation in MATLAB.


    2. Relevant equations
    See above


    3. The attempt at a solution
    When derivating y(t) we get

    [tex]y'(t)=Ae^{-\frac{b}{2m}t}(-\frac{b}{2m}cos(\omega't+\phi)-\omega'sin(\omega't + \phi))[/tex]
    This, together with the initial values gives that [tex]A=\frac{1}{2cos(\phi)}[/tex] and [tex]\phi=arctan(-\frac{b}{2m\omega'})[/tex]

    Is this correct? If not, then what is wrong?
     
    Last edited: Apr 5, 2014
  2. jcsd
  3. Apr 5, 2014 #2

    TSny

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    Homework Helper
    Gold Member

    This looks correct to me. As a check, you should see that your plot of y(t) satisfies the initial conditions.
     
  4. Apr 5, 2014 #3
    Ok, good. Then in other words, we get the following equation: [tex]y(t)=\frac{1}{2cos(arctan(-\frac{b}{2m\omega'}))}e^{-\frac{b}{2m}t}cos(\omega't + arctan(-\frac{b}{2m\omega'}))
    [/tex]
    Right?

    Now I wonder, how can we plot this in MATLAB? Can it be written just like it's written here? Because when I try I don't get a damped oscillation, but an undamped one. What is wrong then?
     
    Last edited: Apr 5, 2014
  5. Apr 5, 2014 #4

    TSny

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    Gold Member

    Yes.

    I would need to see your code. I don't have MATLAB, but when I plot the function using other software, it looks OK.
     
  6. Apr 5, 2014 #5
    Could you please post your code for this? I will try some more and if I still don't manage I will post my code afterwards.
     
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