1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar

    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook