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Harmonic Oscillators Problems

  1. Nov 11, 2009 #1
    1. The problem statement, all variables and given/known data

    1. A 0.5 kg mass extends a spring 1 cm. What is the frequency of oscillation of this mass
    and spring?
    2. A 1 m stick is used as a simple pendulum with a 3 kg weight on the end. What is its
    period of oscillation?
    3. The same meter stick is used as a rigid pendulum with no weight. What is its period?

    2. Relevant equations

    F = −kx = ma.
    x = Asin(wt) .
    w = sqrt(k/m)
    w = 2pie/T
    v = Awcos(wt) .
    vmax= Aw.
    a = −A^2sin(wt) .
    amax= wvmax=Aw^2.
    t = Ia
    t = −FLsin(theta) = −mgLsin(theta) = −mgL(theta)
    I = mL^2
    theta = Asin((2pie/T)*t)
    T = 2pie*sqrt(L/g)
    2pie/T =sqrt(3g/2L)
    3. The attempt at a solution

    1. w = [tex]\sqrt{k/m}[/tex]
    w = [tex]\sqrt{.01m/.5kg}[/tex]
    w = 0.1414rad/s

    2. T = 2*[tex]\pi[/tex] *[tex]\sqrt{L/g}[/tex]
    T = 2*[tex]\pi[/tex] *[tex]\sqrt{1m/9.8m/s^2}[/tex]
    T = 2.007 s

    3. 2*[tex]\pi[/tex]/T = [tex]\sqrt{3g/2L}[/tex]
    2*[tex]\pi[/tex]/T = [tex]\sqrt{3(9.8)/2(1)}[/tex]
    T = 2*[tex]\pi[/tex]/3.834
    t = 1.6388s

    Can someone check my work?
  2. jcsd
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