Period and amplitude of oscillations.

[deezy]

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.

Homework Equations

$$E_i = \frac {1}{2} m_A v^2$$
$$E_f = \frac {1}{2} k A^2 + \frac {1}{2} (m_A + m_B) v^2$$

The Attempt at a Solution

I attached the image of the problem at the bottom.

Trying to find the amplitude of oscillations... I tried $$E_i = E_f$$.

$$\frac {1}{2} m_A v^2 = \frac {1}{2} k A^2 + \frac {1}{2} (m_A + m_B) v^2$$
$$200 = 400A^2 + 400$$

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?

 

[deezy]

Never mind, I figured out what I was doing wrong.

First you consider the initial and final momentum...
$$p_i = p_f$$
$$m_A v_i = (m_A + m_B)v_f$$

Solve for $$v_f$$...

Then $$\frac {1}{2} kA^2 = \frac {1}{2} (m_A + m_B) v^2$$.