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31 March, 07:18

A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 2 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g=980 cm/s^2.

Set up a differential equation with initial conditions describing the motion and solve it for the displacement s (t) of the mass from its equilibrium position (with the spring stretched 3 cm).

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  1. 31 March, 07:40
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    Let s be displacement from equilibrium position. Restoring force

    m d²s / dt² = - k s

    d²s / dt² = - k / m s

    Put k / m = ω

    d²s / dt² + ω² s = 0

    The solution of this differential equation

    = s = A cosωt

    Now when t = 0, s = 2 cm

    A = 2 cm

    Putting the values we have

    2 = A cos 0

    A = 2 cm

    s (t) = 2 cos ωt
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