physics

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a pendulum with a length of .600 m has a period of 1.55 s. what is acceleration due to gravity at the pendulums location

  • physics -

    potential energy = m g h = m g L (1-cosA)

    if angle A is small, cos A = 1 - A^2/2 +...
    so
    Pe = m g L A^2/2

    kinetic energy = (1/2) m v^2 = (1/2) m L^2 [dA/dt]^2)

    if A = sin wt
    dA/dt = -w cos wt

    max potential energy at top = max Ke at bottom

    (1/2) m L^2 w^2 = (1/2) m g L

    w^2 = g/L which by the way is in your book

    g = L w^2
    but w = 2 pi /T since when t = T, the angle w t must be 2 pi, full circle

    g = L (2 pi)^2 / T^2
    here L = .6 and T = 1.55
    so g = 9.85 m/s^2

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