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Simple Harmonic Motion, Finding Time

  1. Apr 28, 2008 #1
    [SOLVED] Simple Harmonic Motion, Finding Time

    1. The problem statement, all variables and given/known data

    A 0.400 kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm.

    Calculate the time interval required for the object to move from x = 0 to x = 4.00 cm.


    2. Relevant equations
    The relevant equations for this should be:

    x = Acos(ωt)

    w = [tex]\sqrt{k/m}[/tex]


    3. The attempt at a solution

    You should be able to solve the above equation for t...

    cos(ωt) = x/A
    ωt = arccos(x/A)
    [tex]t = arccos(x/A)/\sqrt{k/m}[/tex]

    Plugging in the following values:

    x = 4 cm
    A = 10 cm
    k = 8 N/m
    m = 0.400 kg

    I get that t = .259s which is not right. Where am I going wrong?
     
  2. jcsd
  3. Apr 28, 2008 #2

    Erf

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    Just as a quick notice, your "plug in" values have inconsistent units... you have both cm and m
    Would that fix the problem?
     
  4. Apr 28, 2008 #3
    That shouldn't matter because the units for the arccos(x/A) should simply cancel each other out.
     
  5. Apr 28, 2008 #4

    alphysicist

    User Avatar
    Homework Helper

    Hi Ithryndil,

    The problem is your trig function cos(w t). That function at t=0 indicates that the particle is at the positive amplitude, so you found the time to go from x=10 cm to x=4 cm.

    If instead you use a sine function, since it is zero at t=0, you should be able to follow the rest of your procedure. (Or you could put a phase shift [itex]\phi[/itex] into your cosine function to make it act like a sine function.)

    But whenever your problem depends on the oscillator being at a specific position at t=0 (and perhaps a specific velocity direction), you must make sure that your trig function has that same behavior.
     
  6. Apr 28, 2008 #5
    Ok. Thank you for your help. That worked.
     
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