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  1. K

    Equation of motion coursework

    Homework Statement I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with. I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper. Homework...
  2. K

    Big O notation

    Homework Statement Taking e to be small, we have been given these two formulas to prove m1 = \frac{-1+\sqrt{1-4e}}{2e} = \frac{-1+(1-2e+O(e^2))}{2e} = -1+ O(e) m2= \frac{-1-\sqrt{1-4e}}{2e} = \frac{-1-(1-2e+O(e^2))}{2e} = -1+ O(1) Homework Equations The Attempt at a Solution...
  3. K

    Integrating e^-4tsint

    Homework Statement Integrating -e-4tsint Homework Equations Our tutor suggested we did this by integrating by parts in a cyclic fashion and things would cancel out The Attempt at a Solution Taking u = sint t; thus u'=cost And v'=-e-4t; thus (1/4)e-4t \int-e4tsint =...
  4. K

    Legendre's equation

    Homework Statement Obtain the recurrene relation between the coefficient ar in the series solution y= (between r=0 and \infty) \Sigma arxr to (1-x2)y''-2xy'+k(k+1)y=0 Deduce that if k is a positive integer, then ak+2=0, so that the equation possesses a solution which is a polynomial...
  5. K

    Heaviside function and dirac delta

    Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...
  6. K

    Laplace Growth restriction

    Homework Statement The condition to be satisfied for a Laplace transform is U(t)<Mekt Homework Equations I am trying to proove that et2 does not satisfy this The Attempt at a Solution It was suggested that we try taking logarithms of both side: t2<ln(Mekt) t2<lnM+lnekt t2<lnM+kt...