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Differential equation

  1. Aug 24, 2016 #1
    1. The problem statement, all variables and given/known data
    The equation of motion of a particle is given by the differential equation ##\frac{d^2x}{dt^2} = -kx##, where ##x## is the displacement of the particle from the origin at time ##t##, and ##k## is a positive constant.

    1. Show that ##x = A\cos{(kt)}+B\sin{(kt)}##, where ##A## and ##B## are constants, is a solution of the equation of motion.
    2. The particle was initially at the origin and moving with velocity ##2k##. Find the constants ##A## and ##B##.

    2. Relevant equations


    3. The attempt at a solution
    I know for 1. just show LHS = RHS which I have done but a little lost on 2.
    Please help!!!
     
  2. jcsd
  3. Aug 24, 2016 #2

    blue_leaf77

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    That means ##x(0)=0## and ##x'(0) = 2k##. With these two equations, you are supposed to express ##A## and ##B## in terms of the known quantities.
     
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