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    coblos's Avatar
    coblos Posts: 1, Reputation: 1
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    #1

    Nov 9, 2008, 03:42 AM
    simple harmonic oscillation problems
    I have a physic problems for university
    please help me if you could solve this problem.
    I really appreciate your help
    thank you

    A weight which mass 1 kg, tied to a spring with spring constant (k) = 100 pi^2 N/m.
    The spring had a simple harmonic oscillation (in cosinus).
    At t(time)= 0 s, the displacement (x) is 0.032 m and the velocity is 0.24 pi m/s toward negative x axis.

    Find:
    a) Maximum displacement(Amplitude) and phase constant
    b)The displacement function (as a function of time x(t))
    c)The acceleration when the displacement is -0.016 m

    Thank you very much
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Nov 11, 2008, 02:06 PM

    The equation of motion is of the form:

    x = A sin(wt + C)

    where A is the amplitude of motion, w is the frequency, and C is the phase shift. You know that for a spring & mass system w = sqrt(k/m). So to define the weight's motion you need to find A and C. You can do this with the two boundary conditions you were given - one of which has to do with the object's initial position (x at t=0) and the other with its initial veocity - you will need to differentiate the equation above with respect to time to get the equation of velocity. So you will have 2 equations and 2 unknowns. Can you take it from here?
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