Recent content by LANS

  1. L

    Geometric Optics - Magnification

    There's 1/d_I + 1/d_o = 1/f (and same for r_I, r_o), and r_I - d_I = 75, I'm just not sure how to approach it algebraically.
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    Geometric Optics - Magnification

    Sorry, I miswrote it. The object and screen moved, mirror stays in the same place.
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    Geometric Optics - Magnification

    Homework Statement A concave mirror forms an image on a screen twice as large as an object. Both object and mirror are then moved such that the new image is 3x the size of the object. If the screen is moved 75cm, how far did the object move? Homework Equations m = image distance / object...
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    Solving second-order ODE with Runge-Kutta 4

    Homework Statement Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4? Homework Equations See above. The Attempt at a Solution Substituting dy/t = z gives \frac{dz}{dt} = 3z - 2ty -...
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    Polynomial finite fields; ElGamal decryption

    Thanks, that helps. Yes, I do know Fermat's little theorem, I feel silly now for not thinking of it.
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    Physics lab practical (Centripetal Force)

    v for centripetal force refers to tangential velocity of the rolling object, so its the velocity of the cork rolling down the ramp, assuming the cork has enough friction against the ramp to not slide.
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    Polynomial finite fields; ElGamal decryption

    Homework Statement Given some ElGamal private key, and an encrypted message, decrypt it. Homework Equations Public key (F_q, g, b) Private key a such that b=g^a Message m encrypted so that r=g^k, t=mb^k Decrypt: tr^-a = m The Attempt at a Solution My problem is finding r^-a...
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    Convergence of a series

    Compare it to \sum \frac{2^n}{3^n} \frac{2^n}{3^n}\cdot\frac{3^n-1}{2^n} \frac{3^n}{3^n} - \frac{1}{3^n} 1- \frac{1}{3^n} With limit n->infinity, this = 1
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    Legendre polynomials and binomial series

    Sorry, I wrote the original question in a slightly confusing way. Anyways, I solved it last night:
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    Legendre polynomials and binomial series

    Homework Statement Where P_n(x) is the nth legendre polynomial, find f(n) such that \int_{0}^{1} P_n(x)dx = f(n) {1/2 \choose k} + g(n) Homework Equations Legendre generating function: (1 - 2xh - h^2)^{-1/2} = \sum_{n = 0}^{\infty} P_n(x)h^n The Attempt at a Solution I'm not sure if that...
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    Hill cipher - two plaintext pairs encrypt to same ciphertext

    Homework Statement Given the following key, find two plaintext pairs that encrypt to the same ciphertext. \begin{pmatrix} 9 & 5 \\ 7 & 3 \\ \end{pmatrix} (mod \ 26) Homework Equations The Attempt at a Solution Let the two plaintext pairs be (a, b) and (c, d). Let the...
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    Momentum conservation of asteroid in a dust cloud

    m(t) = m_{0} - dm*t Thanks, didn't quite think about that one. Forgot to consider that the amount of mass the asteroid picks up in a set amount of time is dependant on its velocity, and is thus not a constant term.
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    Rocket momentum

    Homework Statement A rocket of initial mass m_{0} accelerates from rest in vacuum in the absence of gravity. As it uses up fuel, its mass decreases but its speed increases. For what value of m is its momentum p = mv maximum? Homework Equations Tsiolkovsky rocket equation: v(m) = v_e ln...
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    Momentum conservation of asteroid in a dust cloud

    Note: this is one of the suggested practice problems for my second-year classical mechanics course. Homework Statement A spherical asteroid of mass m_{0} and radius R, initially moving at speed v_{0}, encounters a stationary cloud of dust. As the asteroid moves through the cloud, it collects...