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Mechanical energy of a spring system

  1. Apr 15, 2014 #1
    1. The problem statement, all variables and given/known data
    A damped mass-spring system oscillates at
    285 Hz. The time constant of the system is
    8.8 s. At t = 0 the amplitude of oscillation
    is 1.3 cm and the energy of the oscillating
    system is 36 J.
    Part 1: What is the amplitude of oscillation at t =
    8.7 s?
    Answer in units of cm
    Part 2: How much energy is dissipated in the first
    period (8.7 s interval)?
    Answer in units of J

    Part 3: How much energy is dissipated in the second
    period (8.7 s interval)?
    Answer in units of J


    2. Relevant equations
    A = A(initial) * e-(t/time constant)
    E = E(initial) * e-(t/time constant)

    I followed the method of the attached picture and couldn't get the correct answer.

    3. The attempt at a solution
    Part 1: Answered correctly:
    A(8.7 s) = (1.3 cm) * e-(8.7/8.8) = 0.4837088518 cm

    Part 2:
    Change in mechanical energy between 0 and 7.8 seconds:
    ΔE = -E(initial) * (e-(8.7/8.8) - e-(0/8.8))
    ΔE = -(36 J) * (e-(8.7/8.8) - 1)
    ΔE = 22.604985 J
    Which was incorrect

    Part 3:
    ΔE = -(36 J) * (e-(17.4/8.8) - e-(8.7/8.8))
    ΔE = 8.4109474 J
    Which was also incorrect.
     

    Attached Files:

  2. jcsd
  3. Apr 16, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Check the small print (I can hadly read it): Energy is proportional to A2, so one of your equations isn't right
     
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