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Homework Help: Period and amplitude of oscillations.

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Block “A” is released with initial velocity v=10 m/s. Find the period and the amplitude
    of oscillations after inelastic collision of block “A” with block “B”. The mass of block “A” is
    2 kg, the mass of block “B” is 2 kg. The spring constants of the springs are 100 N/m and 300
    N/m. The surface is frictionless and the springs are massless.

    2. Relevant equations
    [tex]E_i = \frac {1}{2} m_A v^2[/tex]
    [tex]E_f = \frac {1}{2} k A^2 + \frac {1}{2} (m_A + m_B) v^2[/tex]

    3. The attempt at a solution

    I attached the image of the problem at the bottom.

    Trying to find the amplitude of oscillations... I tried [tex]E_i = E_f[/tex].

    [tex] \frac {1}{2} m_A v^2 = \frac {1}{2} k A^2 + \frac {1}{2} (m_A + m_B) v^2[/tex]
    [tex] 200 = 400A^2 + 400[/tex]

    Got stuck here, because when I subtract 400 I get -200 on the left side and I can't take the square root... am I setting this up right?

    Attached Files:

  2. jcsd
  3. Dec 9, 2011 #2
    Never mind, I figured out what I was doing wrong.

    First you consider the initial and final momentum...
    [tex]p_i = p_f[/tex]
    [tex]m_A v_i = (m_A + m_B)v_f[/tex]

    Solve for [tex]v_f[/tex]...

    Then [tex]\frac {1}{2} kA^2 = \frac {1}{2} (m_A + m_B) v^2[/tex].
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