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Period and amplitude of oscillations.

  • Thread starter deezy
  • Start date
18
0
1. Homework Statement
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. Homework 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?
 

Attachments

18
0
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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