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  1. LuccaP4

    Solid-state Physics: Fermi surface and necks in an FCC structure

    Does anyone have some bibliography about necks in FCC structure Fermi surface? I have to solve this problem and I have no idea how to start. Thanks.
  2. LuccaP4

    I 4th-rank isotropic tensor

    I have this statement: Find the most general form of the fourth rank isotropic tensor. In order to do so: - Perform rotations in ## \pi ## around any of the axes. Note that to maintain isotropy conditions some elements must necessarily be null. - Using rotations in ## \pi / 2 ## analyze the...
  3. LuccaP4

    Hamiltonian mechanics: phase diagram

    Okay, then I'll do that. Thanks.
  4. LuccaP4

    Hamiltonian mechanics: phase diagram

    But the statement says to write it in spherical and cylindrical coordinates. I have to build the phase space in that coordinates.
  5. LuccaP4

    Hamiltonian mechanics: phase diagram

    The issue here is that I don't know how to operate the final equations in order to get the phase diagram. I suppose some things are held constant so I can get a known curve such as an ellipse. I attach the solved part, I don't know how to go on.
  6. LuccaP4

    Lagrangian mechanics: central-force-like problem

    Is this valid in every case? In the frecuency ##\omega##, I should evaluate the second derivative in ##r_0##, shouldn't I?
  7. LuccaP4

    Given the following graph, answer the following questions: increasing, decreasing, or constant?

    I'm not really sure, but if in ##x=-6## there is an asymptote, then the function is not defined in ##\left(-\infty,-6\right]##
  8. LuccaP4

    Need help deducing the region for this double integration problem

    You can use inequalities in geogebra as well.
  9. LuccaP4

    Given ##f(x)=3x^5-5x^3##, find all critical points.

    I think it's fine, but I agree with @haruspex that you have to check the factorisation of ##y''##. Just a friendly reminder: there are critical points as well where the derivative doesn't exist. In this case, the first derivative exists for every ##x##, so you don't have to matter.
  10. LuccaP4

    Question about the solution of this system of equations

    As @Mark44 says, its the same expression. An integer ##k## could be positive or negative, so if you take ##2k## or ##-2k##, both determines the same set of integers, which is positive and negative even integers. ##k=\left\lbrace...,-3,-2,-1,0,1,2,3,...\right\rbrace ##...
  11. LuccaP4

    Curve sketching (discussion)

    Be careful! There are 2 types of critical values. First type are the ones that makes ##f'(x)=0## or where the first derivative doesn't exist. Second type are the ones that makes ##f''(x)=0## or where the second derivative doesn't exist. First type critical values could be extremes (maximum or...
  12. LuccaP4

    Given the following graph, state the intervals concave down

    I think is correct. The second derivative in ##x>0## equals ##0## and in ##-6<x<-2## the function is concave up. ## x=-2 ## would be the point of inflection.
  13. LuccaP4

    Lagrangian mechanics: central-force-like problem

    I copy again the statement here: So, I think I solved parts a to c but I don't get part d. I couldn't even start it because I don't understand how to set the problem. I think it refers to some kind of motion like this one in the picture, so I'll have a maximum and a minimum r, and I can get...
  14. LuccaP4

    D'Alembert's principle on a pulley system

    I solved it, thanks for the help. I attach the entire solution, if anyone is interested.
  15. LuccaP4

    D'Alembert's principle on a pulley system

    Yes, I typed it wrong (copy-paste from above :doh:) but wrote it right. The numerator is negative. So if they're equivalent, I'll try simplifying the result and go on with the other accelerations. Thanks for your answer!
  16. LuccaP4

    Is it possible to build a laser from a light bulb?

    If you want to do this, I think you have to make a parabolic mirror with a converging lens in the focus. Nevertheless, you just will take a lot of energy and it wont work as a laser. The converging lens will give you a point where all beams come together, while the laser is a punctual emission...
  17. LuccaP4

    Personal project idea that I'm not sure will work -- Help please with a robot parrot project

    Thanks for the data. Maybe the battery pack would make the difference. Also Arduino is cheaper. Nice, I'm searching it. Edit: This is pretty interesting. https://create.arduino.cc/projecthub/techno_z/program-your-arduino-from-your-raspberry-pi-3407d4
  18. LuccaP4

    Personal project idea that I'm not sure will work -- Help please with a robot parrot project

    I suppose the first thing to do is studying the parrot skeleton and the types of movement in order to replicate the joints. If you know about programming, maybe Raspberry Pi would be better than Arduino, but it depends on what do you want the parrot to do.
  19. LuccaP4

    D'Alembert's principle on a pulley system

    Thanks for the data! I'll learn it for the next time.
  20. LuccaP4

    D'Alembert's principle on a pulley system

    I struggled just to write the principle on Latex. I'll try uploading a better image. Edit: It won't let me upload the images beacause they're too big. Guess I'll type it.
  21. LuccaP4

    D'Alembert's principle on a pulley system

    This is the problem's picture: My problem is that what I got for one acceleration (m3's) via Newton's equations is not the same as via D'Alembert's principle (I've checked on my PC if they are the same expression). I can't find the mistake. Any suggestion is welcome. I attach pictures of what...
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