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  1. S

    Is impulse an approximation?

    Are you saying that practically speaking we can't know F(t) or T(t)? Can you elaborate on the relativistic implications? I am very determined to fully understand this concept. Thank you kindly.
  2. S

    Is impulse an approximation?

    Hi all, I am reading a book on spacecraft engineering in the section about trajectory dynamics. They define linear and angular momentum as: ##I = \int_{0}^{\tau}{F}dt## (Linear Momentum) ##L = \int_{0}^{\tau}{T}dt## (Angular Momentum) But they (and so many other sources) always mention the...
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    Derivative of a Convolution

    Oh I see what you mean. Thanks for the clarification. I'm just not use to this notation :)
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    Derivative of a Convolution

    Sorry I'm not familiar with your method. I don't understand why you substitute "t+δt" for t. What approach are you using here? Could you elaborate or direct me to some further reading? Cheers :)
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    Root Locus Asymptotes

    When sketching a root locus of a simple closed loop negative feedback system (with positive gain K).... if you have more poles than zeros, we know that they will tend towards infinity along some asymptotes. How do you know which pole will travel along which asymptote? For example in the...
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    Derivative of a Convolution

    Hi, I want to verify that the form of a particular solution satisfies the following ODE: v' + (b/m)v = u/m with vpart= ∫e-(b/m)(t-r) (u(r)/m) dr where the limits are from 0 to t So I tried to differentiate v with respect to t, in order to substitute it back into the equation. But, how do...
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    Taking moments about a point

    Conceptually, what does it actually mean to take the 'moments about a point' on a body, even if that point is not the center of rotation of the body (center of mass say). For example, we could take the moments about a point not even 'in' the body, so what does this value represent? I am...
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    Quick spherical coordinate question

    Thanks so much! I just wasn't visualizing it properly, and I used those values and it seems to be working :D
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    Quick spherical coordinate question

    So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...
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    Systems of ODE: Converting complex solution to real

    I dont think so, because it has to still span the solution space, and merely dropping the imaginary parts will not ensure this.
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    Systems of ODE: Converting complex solution to real

    1. Homework Statement So, I have found a general solution to a system of linear first order ODE's and this is what I got: X = c1v1e^(-1+2i)t + c2v2e^(-1-2i)t where v1 = [-1+2i, 5], v2=[-1-2i,5]. The question is, how do I now change this solution into its real equivalent? i.e. I dont want any...
  12. S

    Entropy of an ideal gas

    1. Homework Statement A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process. Is there a way to calculate this using the thermodynamic identity (ie. without...
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    Representing a wavefunction using bases

    Thanks for the help guys :)
  14. S

    Representing a wavefunction using bases

    Could someone please elaborate on this and show exactly how we come up with the coefficients being the relative probabilities..? Just keep it 1dimensional.Thank you!
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    Scattering by a potential

    Re: "Scattering" by a potential Ok, but how physically does this make sense? How does the fact it goes past a potential change its path? I suppose I still don't fully understand what potential wells represent physically.
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    Scattering by a potential

    Re: "Scattering" by a potential What do you mean when you say transmitted/reflected? If we are talking about a beam of electrons moving towards an attractive square potential (-ve well), what is meant by whether it is transmitted or not..? (In 1D)
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    Scattering by a potential

    "Scattering" by a potential When we have an unbound particle travelling past a potential well, what does it mean when it is said that the potential well will "scatter" the particle?
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    Bosons and quantum states

    Thanks for the detailed response Mike. I can see how just statistically working it out, it shows that bosons are more likely to be together... However, I came across this article which describes a sort of 'avalanche' process: http://eve.physics.ox.ac.uk/Personal/ruprecht/BEC/pw2/pw2.html...
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    Phase-Space (density?)

    So I think I have the basic idea of what phase-space is... basically a way of representing all possible states of a system in some n dimensional space. So, what then, is phase-space density?
  20. S

    Bosons and quantum states

    If we take most of the energy out of the system so theres practically no energy, then there may be a few bosons in higher energy states but most of them will be in the lowest possible state, that is what I got from it. Are you saying there is some other reason why they go to the ground state?
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    Bosons and quantum states

    Oh, so the fact that we have lowered them to around ground state means most of them will, statistically, be in the ground state. So this tendency is purely a statistical one?
  22. S

    Bosons and quantum states

    Oh so its just like the basic statistical physics explanation... am I right to say however, that they all want to occupy the GROUND state? rather than just be together in any state?
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    Bosons and quantum states

    I am doing some research on Bose-Einstein condensates and was hoping someone could give me a non-mathematical reason as to why bosons 'want' to occupy the same ground state. I think its details come from Bose-statistics, but is there a simplified way of explaining it? Thanks
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    Representing a wavefunction using bases

    I had a feeling that was the answer. Ok, well, how do we know that the expansion coefficients are the relative probabilities? is it because we observe this?
  25. S

    Representing a wavefunction using bases

    Can someone please explain why the representation of a wavefunction as an expansion of basis eigenfunctions actually gives us something of physical meaning? For example, it can tell us the probabilities of measuring a particular eigenvalue (depending on the expansion coefficients).... I mean its...
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    Differentiating complex numbers?

    I am not sure whether there is any difference between differentiating complex and real numbers... I am just trying to differentiate: e^(2+3i)x = (2+3i)e^(2+3i)x Is this correct? I have a feeling its not this simple.
  27. S

    Parametric equations and derivatives

    Thankyou!
  28. S

    Parametric equations and derivatives

    Where did this come from? I cant see why we should add the contributions of each?
  29. S

    Parametric equations and derivatives

    Just a quick question... if we have f(x,y,z) and x(t), y(t), z(t), without substituting in what x y and z are in f, how do we calculate df/dt?
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    Potential Wells

    Hi Shyan, thanks so much. Now I have another question, if we have a potential well diagram as I showed above and there is a particle with more energy than the top of the well, why is it that we know for sure it wont go into that well. I mean, as you said there are forces causing this potential...
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