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Homework Help: Simple Harmonic Motion of a Particle

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data

    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



    2. Relevant equations

    None

    3. The attempt at a solution


    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.
    I was thinking to use the Instantaneous Velocity formula (Vins = omega {square root[(amplitude)^2 - (displacement)^2]} but that isn't giving me the correct answer.

    Thanks for your help in advance!
     
  2. jcsd
  3. Sep 19, 2010 #2

    kuruman

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    Gold Member

    You need to write down an expression that gives you the position x(t) as a function of time. Take the derivative to get the velocity v(t) as a function of time. From that you can easily find the speed at t = 1.0 ms.
     
  4. Sep 19, 2010 #3
    Thanks, but can you show me the steps?
     
  5. Sep 19, 2010 #4
    x = x0 sin (omega t)

    If you differentiate this function with respect to time, you'll get the function of Velocity.

    Both equations (Instantaneous and function of time) should give you the same answer, so check your workings again.
     
    Last edited: Sep 19, 2010
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