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Math Help - Mechanical vibrations

  1. #1
    s7b
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    Mechanical vibrations

    I was wondering if anyone would be able to start me off on this question;

    A Weight stretches a spring 3 inches. It is set in motion at a point 4 inches below it's equilibrium position with zero velocity.
    -Find the max amplitude
    -Find the max velocity
    -When does it reach it's highest point
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  2. #2
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    for an ideal spring ...

    Hooke's law (scalar version) ... F = kx

    F = mg = weight of the mass
    x = spring displacement
    k = spring constant

    mg = kx

    k = \frac{mg}{x}

    amplitude of oscillation, A = max displacement from equilibrium (was given to you).

    angular frequency, \omega = \sqrt{\frac{k}{m}}

    period of oscillation, T = \frac{2\pi}{\omega}

    time from the bottom to the top would be half a period.

    max speed, v_{max} = A\omega, occurs as the mass passes back and forth through equilibrium.
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