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Homework Help: Harmonic Motion Spring Constant

  1. Jun 4, 2014 #1
    Hello I was given this problem, and I have two possible answers and I really just need someone to verify which one is right, or at least in the right direction. Thanks!

    1. The problem statement, all variables and given/known data
    A cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes simple harmonic motion with a period of 4 seconds. Its mass is 2kg. Its maximum displacement from rest position is 1.8m. Calculate the spring constant and provide units.

    2. Relevant equations
    Given in problem statement:
    ω² = (F/s)/m
    What I found online:
    k = -F/x

    3. The attempt at a solution
    Using k = -F/x ( But I'm not sure I was suppose to use this equation.
    k = - F(force=ma)/x(displacement)
    k = - 2*9.8/1.8
    k= - 196/1.8
    k= 108.89 n/m

    Using ω² = (F/s)/m I came up with
    ω² = (F/s)/m
    (196/4)/2 = 24.5 n/m
  2. jcsd
  3. Jun 4, 2014 #2


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    How does the gravitational acceleration come in? The cart is on an air-track, and floats. It does not fall!

    You have to know the meaning of the symbols in the formula you are using. What are F, s, ω?

  4. Jun 5, 2014 #3
    F = force
    s = Seconds
    omega is angular velocity
    I pretty sure those are right, not sure about s though.

    And about the gravitational acceleration, I guess that was a mistake haha
  5. Jun 5, 2014 #4


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    You used mg = 196 N for the force. It is wrong.
    Read about SHM (simple harmonic motion) in your book or lecture notes. What force acts to objects performing SHM? How is ω related with the spring constant (k) and the mass (m)?

  6. Jun 5, 2014 #5
    okay so ω is angular frequency, s was displacement.
    ω = spring constant (k) / mass (m)
    So if I want the spring constant I would need to work out ω and then ω * m which would equal the spring constant?
  7. Jun 5, 2014 #6
    ω also equals 2π/f, 2 * pi / T
    frequency = 1/T
    Last edited: Jun 5, 2014
  8. Jun 5, 2014 #7
    ω = 2 * 3.1415 / 4 (T)
    ω = 1.57 rad/s
    k = ω * m
    k = (3.14²) * 2

    k = 6.28 n/m
    Okay I think that this is the answer! Please check what I've done =)
  9. Jun 5, 2014 #8


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  10. Jun 5, 2014 #9
    Okay hows this?
    ω² = (F/s)/m
    ω² =k/m

    ω = 2π/T
    ω = 2 * 3.1415 / 4 (T)
    ω = 1.57 rad/s
    ω convert to ω²
    ω² = 2.46
    k = ω² * m
    k = 2.46 * 2
    k = 4.93 n/m
  11. Jun 5, 2014 #10


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    It is much better.:smile: But "newton", the unit of force, is abbreviated with capital N.

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