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?

 

[rezeew]

Based on the information provided, it seems like the waveform is representing an alternating current (AC) signal. The graph shows the amplitude of the current over time. The filled nodes indicate the peaks of the waveform, where the current reaches its maximum value, and the open nodes indicate the troughs, where the current reaches its minimum value.

As for the time interval, it is correct to assume that one cycle of the waveform takes 3 seconds, as indicated by the filled and open nodes at t=0, 1, and 2 seconds. This means that the cycle does not repeat every 2 seconds.

It is important to note that the amplitude of the current is not constant throughout the cycle. It starts at a value of 2, decreases to -2, and then returns to 0. This shows that the current is alternating between positive and negative values.

I hope this helps clarify how to interpret the graph of the waveform. If you have any further questions, please let me know.