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SHM find F, with A, v, and m

  1. Feb 28, 2010 #1
    I feel like an idiot for not being able to answer this question, it seemed so simple yet so complicated in my head.

    1. The problem statement, all variables and given/known data
    Have to find frequency, given the amplitude, velocity, and mass.
    I don't have numbers as it was off an exam I just took. Guessing it was v=5 m/s; A=10m; and m=3kg.


    2. Relevant equations
    I was thinking of taking the derivative of the SHM eq x(t) = Asin(wt) but then I wasn't sure if I could calculate the spring constant with F = -K(xo - xf).


    3. The attempt at a solution
    My attempt was guessing, but if we threw in numbers, A=10m, v=5m/s, m=3kg...
    x(t) = A * sin(wt)
    w = 2 * PI * f
    x(t) = A * sin(2 * PI * f * t)
    v(t) = 2 * PI * f * A * cos(2 * PI * f * t)
    t = 0
    5 = 2 * PI * f * 10 * cos(2 * PI * f * 0)
    5 = 2 * PI * f * 10 * 1
    5 = 20 * PI * f
    5 / (20 * PI) = f
    f = 0.0795Hz

    or..

    F=-K(x-xo)
    F = 3*9.8 = 29.4
    x = 10
    xo = 0
    K = 2.94 N/m
    f = (1 /( 2 * PI )) * sqrt( k / m)
    f = 0.159 * sqrt (2.94 / 3 )
    f = 0.1576 Hz

    Would love to know the correct way to do this, as I'm confused..
     
  2. jcsd
  3. Feb 28, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    Using F=kx would depend on how the spring is orientated. But I would use your first method.
     
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