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Math Help - Damped Harmonic Oscillation Question

  1. #1
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    Damped Harmonic Oscillation Question



    If a marble is placed on the end of a horizontal oscillating spring and the harmonic horizontal position of the marble as a function of time is given as :

    If x = A ( 2 pi f t)

    where A is amplitude
    f is frequency

    and t is time in seconds
    If the spring oscillates every 0.5 seconds and has a maximum displacement of 0.2 m

    what is the frequency?
    what is the velocity as a function of time ?

    how do you write the equation in the form given above for the position of the marble as a function of time ?
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  2. #2
    Super Member Showcase_22's Avatar
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    Isn't it x=A \cos ( 2 \pi ft)?

    If the spring oscillates every 0.5 seconds, then isn't the frequency just \frac{1}{0.5}=2Hz?

    The velocity is v=\frac{dx}{dt}=-2 \pi Af  \sin (2 \pi f t).

    From here you can normally use the initial conditions to find A. When t=0, v=0.
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