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Question about driven coupled oscillator.

  1. Jul 22, 2012 #1
    How does one go about plotting the effects of the frequency of the driving force vs the amplitude of the masses in a system such as the one pictured below?

    Assume that I have already figured out what my two angular frequencies are, and the amplitues under driven force (the actually equations for the amplitudes are quite lengthy and I will try to refrain from writing it all out here)

    The two frequencies for this system are[itex]ω± = (1/2)(2ω^2p + ω^2s)±(1/2)\sqrt{ω^4p + w^4s} [/itex]

    and I can plug these into our equations for the amplitude of my oscillators. However I find that there are some irreducible terms such as w^2p which are left behind.. I just can't seem to imagine how I am supposed to generate a graph Amplitude vs ω
     

    Attached Files:

  2. jcsd
  3. Jul 22, 2012 #2

    Simon Bridge

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    The picture appears to show a mass on a spring with a pendulum coupled in.
    It's like this one (unfortunately unfinished).

    How is it being driven? By pushing the wall back and forth?
    What is p and s? Your dimensions don't look like they match up - maybe I'm missing the context?
     
  4. Jul 23, 2012 #3
    wp is the frequency of the pendulum and ws is the frequency of the spring.
     
  5. Jul 23, 2012 #4

    Simon Bridge

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    <facepalm> subscript failure!
    Here, let me:[tex]ω_\pm = \frac{1}{2}(2ω^2_p + ω^2_s) \pm \frac{1}{2}\sqrt{ω^4_p + w^4_s} [/tex]
    ... OK, but you still have frequency on the LHS and frequency-squared on the right. Or did I miss something else and really need to get more sleep?

    Are ωp and ωs the actual frequencies the components oscillate at or are they the natural frequencies without interference?
     
  6. Jul 23, 2012 #5

    Simon Bridge

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    Oh wait! you are saying that since you don't have any values for some terms, you don't see how to plot amplitude vs frequency - since that would normally require actual numbers??
    Is that right?
     
  7. Jul 23, 2012 #6
    Well I am just saying that the plot is somewhat complex.. I notice that the key points where the shift in the graph occur are when ω is equal to exactly our ω_, our ω+, and our ωp terms.

    However I don't know what to do in-between, and I am not sure how using just this and our equations for the amplitude of the block/pendulum we are supposed to generate a sufficient graph.

    I can link you to the answer key for this problem set I was working on so that you can see for yourself.

    Thanks.
     
  8. Jul 24, 2012 #7

    Simon Bridge

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    Hint: you can type a subscript with sub tags or in latex like this:
    Code (Text):
    [noparse]
    ω[sub]p[/sub], ω[sub]±[/sub]
    [itex]\omega_p[/itex], [itex]\omega_\pm[/itex]
    [/noparse]
    Which renders as:
    ωp, ω±
    [itex]\omega_p[/itex], [itex]\omega_\pm[/itex]
    What are the graphs supposed to demonstrate?

    Normally I'd just invent some values and use a computer to generate the plots ... adjusting the values to bring out the features I want to show.
     
    Last edited: Jul 24, 2012
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