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Conservation of energy question

  1. Mar 3, 2015 #1
    1. The problem statement, all variables and given/known data
    A mass is attached to a spring (on a wall) of constant 100 N/m. The mass is 1 kg. The mass has an initial position of 3 m from the equilibrium position and is given an initial velocity of 5 m/s. Find the period and amplitude of oscillations.

    2. Relevant equations

    Period: T=2(pi)(m/k)^(1/2)

    Spring potential energy: (1/2)*k*x^2

    Spring kinetic energy: (1/2)*m*v^2

    3. The attempt at a solution

    The period is the equation above, so T = 2(pi)(1/100)^(1/2)=0.63 s

    I'm having a bit of trouble with the amplitude. After awhile, I realized that the potential energy is at a maximum at the amplitude and is equal to the total energy because the mass is at rest at the amplitude.

    The total energy from the initial conditions is the sum of the initial potential and kinetic energies

    (1/2)*100*3^2+(1/2)*1*5^2 = 462.5 J = (1/2)*k*A^2 = (1/2)*100*A^2, so A = 3.04 m.

    Is that work right? Seems like the amplitude should be farther than only .04 m, but I guess that's the way the numbers work out.
     
  2. jcsd
  3. Mar 3, 2015 #2

    BvU

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    Don't see anything wrong with your result: Amplitude is 3.04 m. Note that the 12.5 J from kinetic energy is only a small fraction of the 450 J from spring energy.

    Isn't it nice that you don't have to ask which way the initial 5 m/s is ? (stretching further or towards equiilibrium position)
     
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