Video

Thanks! I hope this doesn't make you give up though! I'm sure there are many different ways to approach this problem :)

Glad you think so!

Oh interesting! I personally haven't even thought about proving this for complex numbers! Good luck

Thanks 🙏

Unfortunately not. I disassembled it to make other robots :(

@@virtually_passed Do you realize people would buy that that machine on amazon? It like a machine that prints money.

Great questions! 1) you'll typically have a matrix FRF function in that case where each element of the FRF will relate one specific input to one specific output. An important caveat here is that this only applies for linear systems where the superposition principal can be applied.

In answer to your second question: there's a lot of information to unpack about phase but some key insights are: when resonance occurs you will be neither in phase nor out of phase with the input. It'll be at 90 degrees. After resonance you will be at 180 degrees phase which implies that you're fully out of sync with the input. Before resonance you will be at 0 degrees phase which implies you're fully in sync. If you have a multi degree of freedom system though then it becomes a bit more difficult. You can use the bode gain phase relationship to protect how phase relates to gain

Thanks for the feedback: in case you're curious I've made another video proving the same thing in a more intuitive way: czcams.com/video/vyBkvGnPwJk/video.html

@@virtually_passed Oh, thank you! That's what I meant, Very intuitive, clear and convincing! beatuful, thank you

Try emailing me: virtuallypassed@gmail.com

Thanks :) 🙏

Thanks a lot 😊

I agree, it seems like a natural progression. However formulating the problem as an fft problem is very difficult in my view :)

@@virtually_passed indeed! There might be some insight to gain in “simple pattern synthesis for complicated arrays” by RF get down here on CZcams - but I haven’t investigated too much into the usability of the method in your case

Mind = blown! 🤯 Yep, and there's another method using the radon transform which I talked about in my latest video :)

Welcome 😁

🙌🙏

This follows from the derivative: d/dx(f(x))^n = n f(x)^n-1 f'(x)

@@virtually_passed I see. Thank you! (I’ve just been presented with the piece I was missing here: the algebraic proof of the chain rule. 😊)

This is a very interesting idea. I'll be honest with you that I haven't fully solved the color issue. It's very complicated since order highly affects the outcome in a very nonlinear way. So far I found CMYK works quite well in a set order but I'm sure it can be improved.

Lol, how do you say it?

Good question. You can model the line as a Dirac delta function. In which case, the radon transform of this yields 1/abs(sin). However, in reality the line will have some width. I've tried modelling the line with a box profile, triangular profile and oval profile, but all of the radon transforms of these profiles are very complicated and slow to implement numerically. In the end I used a mathematical hack to make the Dirac delta function have thicknesses. Does that answer your question

@@virtually_passed kind of. I was thinking that given a line, there's exactly one value for theta 1 and theta 2 where it overlaps, and for all the others values of thetas, the function in integral to compute the radon transform is 0 at almost every point Do you compute the radon transform numerically? Thanks for the video btw!

Hey there, I'm glad you like it. At the moment the script does not output the precise list of nails. That's a more complicated process that I didn't include. However if this is something you're interested in then send me an email at virtuallypassed@gmail.com and I'll try to create a custom script for you that contains it all in one MATLAB file

Good question. When dealing with matrices we can't divide anymore. We need to multiply both sides by the inverse matrix. And this operation is only defined for square matrices. A^T isn't square in general (there could be more rows than columns or visa versa). However, in the very unlikely case that A happens to be square (ie there are just as many unique data points as unknowns) then you can inverse A^T and the pseudo inverse will collapse into the regular inverse of A. Hope that makes sense

Glad to hear it!

I've got another video followup. I've also got details about the Fourier method on my patreon. Spoiler: the radon transform method is better than the Fourier method in my opinion.

And Australian :)

Glad you enjoyed it. I made a follow up video where I ended up using the math from CT scanners!

You're welcome!

Glad it was helpful!

Thanks :)

Thanks! Glad you like it! 😊

Thanks 👍

Microsoft onenote 2016. Although you can use many others like krita or Photoshop

@@virtually_passed Thanks

Nope the amplitude of oscillation decays exponentially with a linear SMD system. The oscillations get smaller. :)

@@virtually_passed Thx for answering. Im beginner but it looks like amplitude of the oscillations gets smaller with tim, but frequencies seem to be bigger and bigger. I guess im wrong but visually that's what it looks like nah ?

Thanks 🙏👍

Thank you padawan

What a great question. For a single dof system you can easily find the damping ratio using the formulas shown. However for a 2 dof system there will be 2 damping ratios corresponding to each mode. You'll have to use something called modal analysis to find these two modes by diagonalizing the equations of motion. Once you have the uncoupled equations of motion you can use the formula shown to each equation to find both damping ratio. Hope that makes sense

Glad you think so!

No problem!

Thanks! All because of your suggestion to change song 😉

Thanks! I coded up the algorithm myself with MATLAB. You can get access to the code via my Patreon :) patreon.com/VirtuallyPassed

Thank you

Sir different shapes also possible ?? Like semi circle, rectangle, ovel and other shapes hapes. ??

@@KeerthiRoyal25 Only circle and rectangle at the moment

Thanks for the advice :) I'll choose a different song next time. Do you have any favorites?

@@virtually_passed not really, idk what the scene is for copyright free music. Main thing is to repeat songs less, since at least subscribers get a lot of shorts with the same audio. Doesn't help that they're enjoyable to watch multiple times, adding to the repetitiveness 😂

x=position, y = velocity :)

Go season

Once you have an ordered list of nails each described with (alpha,s) values, then you need to convert those values to Psi1,Psi2 values using the last formula I derived. Once you do that you'll find that your values will likely not correspond to a perfect equally spaced set of nails, so you'll have to do a linear interpolation. You'll also have to make an algorithm that converts all these individual disconnected lines, into something a single thread can reach. Another alternative is to perform the greedy algorithm in Psi1,Psi2 space.