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Question about how to interpret the graph of this waveform.

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data

    The question is in regards to a homework problem, but I only need clarification on how to interpret the graph of a waveform.

    2. Relevant equations

    N.A.

    3. The attempt at a solution

    N.A.

    I've attached the image. I am assuming that one cycle of the waveform takes 3 seconds, such that i = 2 for one second, then -2 for 1 second, then 0 for one second, and then it repeats.

    I am double checking that the cycle does not actually repeat every 2 seconds such that i = 2 for one second, then -2 for 1 second and then repeats.

    It is probable obvious that the former is the case, but I just want to be sure, because there are only filled or open nodes drawn at t = 0, 1, and 2 seconds.

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



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Oct 5, 2013 #2

    Simon Bridge

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    Graphs have to be interpreted in context of what you want to find out.
    tldr: not enough information.

    You have a graph of the function:
    $$i(t)=\left \{
    \begin{array}{rl}
    0 & : t\leq 0\\ 2 & : 0<t\leq 1\\ -2 & : 1<t\leq 2 \\ 0 & : t > 2
    \end{array}
    \right .
    $$

    Open and closed nodes are inevitable since i(t) cannot have two values at one time.

    Are you told that this represents the graph of one period of a periodic function with a period of 2s?
    The range appears to be from t=-1s to t=+3s - judging by the plotted (solid) line. Maybe the period is 4s? Maybe it is just a couple of pulses? Context is everything.
     
  4. Oct 6, 2013 #3
    The problem states that it is supposed that in a conductor, i(t) has the waveform shown below. Find and graph q(t). I have no problem finding and graphing q(t) I just wasn't sure about what is meant by waveform in this context. I guess I should assume that like you say that this is not a repeating wave, only a few blips?

    My solution assumed that it was a repeating waveform where one cycle of the waveform takes 3 seconds, such that i = 2 for one second, then -2 for 1 second, then 0 for one second, and then it repeats. And is then
    [ floor(t) mod 3 = 0 ] -> q(t) = 2(t - floor(t))
    [ floor(t) mod 3 = 1 ] -> q(t) = 2 - 2(t - floor(t))
    [ floor(t) mod 3 = 2 ] -> q(t) = 0

    But I think you are probably right, the fact that no "nodes" exist on the two ends of the waveform must indicate that
    (t <= 0) -> q(t) = 0
    ...
    (t >= 2) -> q(t) = 0

    Which makes the problem a lot simpler, but then it seams a little too easy.

    The fact that it is said "has the waveform" throws me off because I think of a wave as cyclical, but I suppose a wave form can be any plot over any range right?
     
  5. Oct 6, 2013 #4

    Simon Bridge

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    That's how I'd have interpreted it, yes.

    At t=0, charge starts moving one way, then at t=1 it starts moving the other way, at t=2 the movement stops. That's what the graph is saying. But it does not say that q(t)=0 for t<0 or t>2. It says that dq/dt=0 at those times.
    Unless you happen to know q(0)=0 or something?
     
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