Is it possible to plot this graph by applying the laplace function in MATLAB to the equation?

Our teacher tasked us to plot the graph by applying laplace transform on the equation. That's all the given and objectives. Nothing more, nothing less. Is it possible?

[Star Strider]

What is the plot a function of? (The plot is too small and the resolution is too coarse. I cannot read the x-label even if I enlarge the plot.)

Do you have values for the constants?

How are and related?

[Harry Louise Plasabas]

That's the thing. We were not taught about anything related to that and just directly asked us to plot the graph using laplace transform function on the equation. To answer your question to the best of my knowledge, the plot is (r, amplitude) where r is maybe arbitrary (?) There were no values for the constants, we were only given the equation and the graph. I1 and I2 are currents from a resonance transformer circuit.

[Sam Chak]

Hi @Harry Louise Plasabas

Now you told and are currents. How do you expect us to know this from your original post? What exactly is ? The amplitude of what?

But I can do something about it. I can refer to the Table of Laplace Transform, because I'm pretty weak at integration.

Anyhow, the initial values are needed, can you carry on from here? You can also show a portion of your teacher's lecture notes related to the problem, so that we can study how exactly your teacher can solve in such circumstances.

[Harry Louise Plasabas]

This was based on an ebook our teacher told us to download. Our teacher saw the equation and the graph and tasked us to connect the two using laplace function in MATLAB. Answering your question, it was a mistake on my part because I did not label I1(t) and I2(t) as currents. For both r(t) and amplitude, I have no idea considering that it has not been taught to us yet. I'm only assuming r(t) to be t.

The table you referred to me is helpful in solving the laplace of the first two variables in the equation. Our teacher does not have lecture notes to the problem nor we know that our teacher is capable of solving it in such circumstances. Our teacher based our assignment in the ebook that we were supposed to download. If it's okay with you, I can send the portion of the ebook where our teacher told us what to do.

[Star Strider]

If the ebook is freely available (and not copyright-restricted or behind a pay-wall), please upload at least the relevant parts of it here.

[Sam Chak]

It's okay. Show the workings to your teacher and say that you are stuck here because the initial values are needed.

[Harry Louise Plasabas]

This is what got me confused. It says in the book that it requires two equations to formulate the plot. But our teacher specifically said to use the first equation and obtain the plot seen in figure 12.8.5

[Sam Chak]

Aha! The Frequency Response.

[Harry Louise Plasabas]

I hope it helped. We're trying to figure out how to obtain that plot using laplace on the first equation only.

Answer 1

[Sam Chak]

Hi @Harry Louise Plasabas

You can plot Fig. 12.8.5 with this:

r = 0:0.01:2;
I2 = 1./sqrt((r.^2 - 1).^2 + 0.01);
plot(r, I2)
grid on
xlabel('r')
ylabel('amplitude of i_{2}(t)')
title('The resonance curve')

But actually, the values for the parameters M, R, , , , , are not given. For some unknown reasons, your teacher expects (but didn't say it out loud) you guys to cleverly assume the values like the author did:

and .

Perhaps the values can be found in one of the references [24] – [27] cited.

Anyhow, the rest you can follow the steps as explained in detailed by the author.

Guess your teacher wants you guys to follow the steps (in ebook) and demostrate them using syms, laplace, solve, and ilaplace to find the solution in Eq. 12.8.60.

[Harry Louise Plasabas]

Everything you said was duly noted. I'll try this.

Where did you get the value for I2? Can that value be derived from the equation our teacher expected us to perform laplace with?

[Sam Chak]

Hi @Harry Louise Plasabas

I've got the equation for I2 from the caption of Fig. 12.8.5. On the same page, it is briefly explained after Eq. 12.8.61.

In short, I should have plotted I2 based on Eq. 12.8.61, the resonance curve equation. But like I mentioned in the previous post, the values for the required parameters in Eq. 12.8.61 are not given. Hence, the best I can do is follow the resonance curve equation shown in the caption of Fig. 12.8.5.

Hope my explanation is acceptable to you. I believe that the ebook has some examples on how to solve the differential equations using syms, laplace, solve, and ilaplace. Perhaps, your teacher wants you guys to freely assign some values to the parameters so long as they satisfy:

and

implies that .

[Harry Louise Plasabas]

This has been very insightful and I will apply what you told me in making our assignment. Thank you!