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Maximum speed of a spring mass is given by 2(pi)(frequency)(amptitude)?

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that the maximum speed (Vmax) of a mass on a spring is given by 2(pi)(f)(A)


    2. Relevant equations

    E(total) = kA^2

    Vmax = sqrt[2E(total) / m]
    (Because E(potential) = 0 when V is at max, so E(total) = mv^2 / 2 + 0)

    f = sqrt(k/m) / 2(pi)
    k = [(f)(2pi)]^2(m)

    3. The attempt at a solution

    Vmax = sqrt[2(kA^2) / m]
    Vmax = sqrt [2[(f)(2pi)]^2 (m) A^2)] / m]
    Square the [(f)(2pi)]^2, factor in m, factor in 2A^2 and cancel out all m's then sqrt I get:

    2Af2(pi)

    Did I make a mistake somewhere? Or did I go about this all wrong? :/
     
  2. jcsd
  3. Mar 29, 2009 #2

    alphysicist

    User Avatar
    Homework Helper

    Hi zeion,

    I don't think this line is right; you appear to be missing something in this equation. Once you correct that I think you'll get the right answer.
     
  4. Mar 29, 2009 #3
    Oh is it kA^2 / 2?
    Oh if it is then it all makes sense.
     
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