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Homework Help: Simple Harmonic Motion and speed of mass

  1. Nov 30, 2014 #1
    1. The problem statement, all variables and given/known data

    A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal?

    I want to know if it's possible to solve for just a number, that is, not in terms of k and m. Also if my answer is right as it is. Thanks.

    2. Relevant equations

    3. The attempt at a solution

    Force equals ma and also -kx
    ma = -kx
    ma+kx = 0
    x''+(k/m)x = 0

    Solve the differential equation, set x(0) = 0 and set the amplitude to 0.1 (in meters) to yield

    x(t) = 0.1sin(√[k/m]t)

    Differentiate to find v(t) and sub them into the equation

    (1/2)mv2 = (1/2)kx2

    I find t = π/4 and v(π/4) = -0.05√(2k/m)
  2. jcsd
  3. Nov 30, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. Dimensional analysis: you are given a length, and you want a speed; you need a velocity or an acceleration etc. to connect those two dimensions.
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