Question about how to interpret the graph of this waveform.

[Jarvis323]

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.

 

[Simon Bridge]

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.

 

[Jarvis323]

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?

 

[Simon Bridge]

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?