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Oscillation Amplitude

  1. Nov 6, 2015 #1
    1. The problem statement, all variables and given/known data
    A 1.4-kg cart is attached to a horizontal spring for which the spring constant is 60 N/m . The system is set in motion when the cart is 0.27m from its equilibrium position, and the initial velocity is 2.6 m/s directed away from the equilibrium position.

    A. What is the amplitude of the oscillation?
    B. What is the speed of the cart at its equilibrium position?

    2. Relevant equations
    E=K+U

    3. The attempt at a solution
    U=½kΔx2 =½⋅60⋅0.272=2.187J
    K=½mv2=½⋅1.4⋅2.62=4.732J
    E=K+U=½mvf2

    Is this the right way to proceed?
     
  2. jcsd
  3. Nov 6, 2015 #2
  4. Nov 6, 2015 #3

    JBA

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    Your first equations are correct and the K+U for E (the total energy at that point) is correct, but now you need to balance T against the U of the spring at the maximum amplitude of the oscillation.
     
  5. Nov 7, 2015 #4

    haruspex

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    Yes, that will give you the answer to one part. What about the other?
     
  6. Nov 7, 2015 #5
    the Velocity at the equilibrium would be, √(2(2.187+4.732)/1.4)=Ve=3.14m/s
    then E=½mVe2=½kΔX2, this X here would be the amplitude. X=0.324
     
  7. Nov 7, 2015 #6

    haruspex

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    Haven't checked the numbers in detail, but that looks right.
     
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