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Amplitude and Period of Oscillation from Collision

  1. Dec 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to a peg in the table. Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s, and the two masses stick together. What are the amplitude and period of the oscillations that result from this collision?
    Correct Answer: A=0.300 m, T=1.26 s

    2. Relevant equations

    [tex]
    T=2\pi \sqrt{\dfrac{m}{k}}\\
    \dfrac{1}{2}mv^2=\dfrac{1}{2}kA^2
    [/tex]
    3. The attempt at a solution
    [tex]
    m=2 + 2 = 4 \ \texttt{kg}\\
    \dfrac{1}{2}mv^2=\dfrac{1}{2}kA^2\\
    A=\sqrt{\dfrac{mv^2}{k}}\\
    A=\sqrt{\dfrac{(4)(3)^2}{100}}=0.600 \ \texttt{m}\\
    T=2\pi \sqrt{\dfrac{m}{k}}\\
    T=2\pi \sqrt{\dfrac{4}{100}}\\
    T=1.26 \ \texttt{s}
    [/tex]
     
  2. jcsd
  3. Dec 13, 2015 #2
    What is the speed of the combined mass after the collision? Is it still 3m/s?
     
  4. Dec 13, 2015 #3
    Thanks!
    [tex]
    v=\dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = 1.5 \dfrac{\texttt{m}}{\texttt{s}}\\
    A=\sqrt{\dfrac{(4)(1.5)^2}{100}}=0.300 \ \texttt{m}
    [/tex]
     
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