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Amplitude from a Damped Oscillation

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    A damped mass-spring system oscillates at 263 Hz. The time constant of the system is 7.4 s. At t = 0 the amplitude of oscillation is 3.4 cm and the energy of the oscillating system is 11 J.
    What is the amplitude of oscillation at t = 6.7 s?
    How much energy is dissipated in the first period (6.7 s interval)?
    How much energy is dissipated in the second interval?

    2. Relevant equations

    x = A*e^-(b/2m)t*cos√(k/m - b^2/4m^2)t
    ω^2 = k/m
    E = 1/2*k*A^2

    3. The attempt at a solution

    I first found my spring constant k, by E = 1/2*k*A^2. k = 2E/a^2 --> k = 19031 kg/s^2.
    I then used ω^2 = k/m to find my mass. m = k/ω^2 --> m = 0.27514 kg.
    This is where I run into a problem. Where do I go? I think I need to find my "b", the strength or constant of damping force, and then use my given "t" to find the new amplitude. Then continue to the next two questions from there.

    New to the forum so let me know if I am missing something or have done something wrong. Thanks in advance!
     
  2. jcsd
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