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Math Help - Simple Harmonic Motion

  1. #1
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    Cool Simple Harmonic Motion

    A particle is oscillating in simple harmonic motion with period 4.5 ms and amplitude 3.0 cm. At time t = 0, the particle is at the equilibrium position. Calculate, for this particle:

    a) frequency
    b) the angular frequency
    c) the maximum speed
    d) the maximum acceleration
    e) the speed at time t = 1.0 ms

    My Attempt

    a) 220 Hz
    b) 1.4 x 10^3 rad/s
    c) 42 m/s
    d) 5.9 x 10^4 m/s^2


    I am stuck at (e) and just don't know how to do this. Thanks for your help in advance!
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  2. #2
    MHF Contributor Unknown008's Avatar
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    The speed at time t = t is given by:

    v = x_o \omega sin(\omega t)

    You can find the speed now

    I got 1.0 m/s.

    EDIT: This is the wrong formula, the trig function should be cosine instead of sine. (at time t = 0, speed is maximum, hence...)
    Last edited by Unknown008; September 19th 2010 at 06:57 AM.
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  3. #3
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    Firstly there is a "negative / -" sign in that formula and secondly that's not the correct answer I got 41.9 with that formula, don't know how you got 1.0 m/s lol

    The correct Velocity is 7.1 m/s.

    Anymore help guys?
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Sorry, I gave the wrong formula.

    The formula is:

    v = x_o\omega cos(\omega t)

    And I forgot to put my calc mode on radians.

    Yes, I get 7.1 m/s
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  5. #5
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    Oh shoot I think that is what I was doing wrong as well :/ Not changing into radian mode

    Thanks!
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