Block 1 of mass \(m_1\) is released from rest at the top of a rough inclined plane of length \(L\) that makes an angle \(\theta\) with the horizontal. The coefficient of kinetic friction between Block 1 and the incline is \(\mu_k\). At the bottom of the incline, Block 1 smoothly transitions to a horizontal, frictionless surface.

Block 1 then collides with and sticks to Block 2 of mass \(m_2\), which is initially at rest and attached to an ideal, uncompressed spring of spring constant \(k\). The other end of the spring is attached to a rigid wall.