Physics

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If you know that the period of a pendulum is 1.87sec. What is the length of that pendulum? (gravity 9.81m/sec squared)

  • Physics -

    F = m A
    m g sin theta = m a = -m d^2 x/dt^2
    g sin theta = -d^x/dt^2
    for small Theta sin Theta = theta = x/L
    g x/L = -d^x/dt^2
    let x = c sin 2 pi f t
    then v = dx/dt = 2 pif c cos 2 pi f t
    and a = d^2x/dt^2 = - (2 pi f)^2 c sin 2 pi f t
    so
    g /L = (2 pi f)^2
    2 pi f = sqrt (g/L)
    but T = period = 1/f
    so
    T = 2 pi sqrt (L/g)
    1.87 = 2 pi sqrt(L/9.81)
    sqrt(L/9.81) = .2976
    L/9.81 = .088577
    L = .869 meter

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