The ball sticks to block C, then block C collides elastically, head – on with A. if the maximum compression is $x_0$ , the spring constant k is

When a ball sticks to block C, the common velocity is

$m{v}_0+m\times 0=\left(m+m\right)v\Rightarrow v=\frac{v_0}{2}$

Now after the ahed-on elastic collision, block C stops and A acquires velocity $\frac{v_0}{2}$. A the maximum compression, the block move together.

$2m\frac{v_0}{2}+m\times 0=2m{v}^1+m{v}^1\to v^1=\frac{v_0}{3}$

$\frac{1}{2}.2m{\left(\frac{v_0}{2}\right)}^2=\frac{1}{2}\left(2m+m\right)v^{1^2}+\frac{1}{2}k{x}_0^2;k=\frac{m{v}_0^2}{6x_0^2}$