I need to find the equations of motion for the following system.
If $x_1$ is $m_1$'s extension and $x_2$ is $m_2$'s, then, I feel like for $m_1$ we just need to consider $x_1$ giving $$m_1 a_1 = x_1 K_C + x_1 K _B$$ because unless the extensions in both the left and right spring isn't the same, $m_1$ won't remain horizontal,
And for $m_2$, we just need to consider $x_2$ and $x_1$ giving $$m_2 a_2 = K_B (x_2 - x_1) + K_A x_2$$ because both the upper and lower springs exert forces on $m_2$.
But sadly, this isn't correct as this gives all 0 normal modes. Any help on where I went wrong would be really appreciated.