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A 100 g blob is attached to a vertical spring and the spring stretched 4 cm from its original length.calculate the spring constant, k and period, t

  • physics -

    m = .100 Kg
    x = .04 meter
    F = m g = 9.81(.1) = .981 N
    k = F/x = .981/.04 = 24.5 Newtons/meter

    let y = A sin 2 pi t/T
    F = -ky = -kA sin 2 pi t/T

    v = (2 pi /T)A cos 2 pi t/T
    a = - (2 pi/T)^2 A sin 2 pi t/T
    F = m a
    so
    k y = m(2 pi /T )^2 y
    2 pi/T = sqrt k/m

    T = 2 pi sqrt (m/k)
    = 2 pi sqrt (.1/24.5)
    = 0.401 seconds

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