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Finding the total response of an undamped spring mass system

  1. Oct 2, 2016 #1
    1. The problem statement, all variables and given/known data
    spring mass system.JPG

    2. Relevant equations
    The response of a spring mass system can be simplified to equal:
    x(t) = (x0 - (F0 / (k - mω2))cos(ωnt) + (x'/ωn)sin(ωnt) + (F0 / (k - mω2))cos(ωt)

    where
    x & x' are the initial conditions
    ω is the exciting frequency
    ωn is the natural frequency
    k is the spring constant
    m is the mass
    and F0 is the amplification of the applied force

    ωn = √(k/m)



    3. The attempt at a solution
    Given normal initial conditions, x = x' = 0

    x(t) = - (F0 / (k - mω2))cos(ωnt) + (F0 / (k - mω2))cos(ωt)

    and ωn = √(k/m) = 6.325rad / s
    Is there a way to solve for F0 and ω?
     
  2. jcsd
  3. Oct 3, 2016 #2

    Simon Bridge

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    No. Those are arbitrarily supplied by an external agency.
     
  4. Oct 3, 2016 #3
    That's what I thought but someone said you could by substituting the given f (t) with the f (t) for harmonic motion - but it seemed like I still on had one one equation 2 unknowns so it didn't seem possible.
     
  5. Oct 3, 2016 #4

    rude man

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    There are three terms in your "relevant equation". Which one or ones look like they could be affected by gravity alone? Remember initial conditions = 0.
     
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