Question about how to interpret the graph of this waveform.

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Discussion Overview

The discussion revolves around the interpretation of a waveform graph related to a homework problem in electrical engineering. Participants seek clarification on the nature of the waveform, whether it represents a repeating cycle or a series of discrete events, and how this affects the calculation of charge over time.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant assumes that the waveform has a cycle of 3 seconds, with specific values for current at different time intervals, and seeks confirmation of this interpretation.
  • Another participant emphasizes the importance of context in interpreting the graph, suggesting that the period may not be clearly defined and could be longer than 2 seconds.
  • A third participant questions whether the waveform is cyclical or represents a few discrete events, indicating uncertainty about the terminology used in the problem.
  • There is a discussion about the implications of the graph's endpoints, with one participant noting that the absence of nodes at the ends suggests that the current is zero outside the specified time range.
  • Participants express differing views on whether the waveform should be considered periodic or simply a representation of transient events.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the waveform is periodic or represents discrete events. There are multiple competing interpretations of the graph and its implications for the associated charge function.

Contextual Notes

Participants note limitations in the problem statement, including the lack of explicit information about the periodicity of the waveform and the definitions of the terms used, which contribute to the uncertainty in interpretation.

Jarvis323
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Homework Statement



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

Homework Equations



N.A.

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.
 

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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.
 
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?
 
tAllan said:
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?
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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