A block of mass m_1 is fastened to a spring on an incline of angle...

Let $x$ be the compression of the spring at any instant.

The equation of motion for the combined system of mass $(m_1 + m_2)$ is:

$kx - (m_1 + m_2)g \sin\theta = (m_1 + m_2)a$

where $a$ is the acceleration of the blocks up the incline.

The acceleration is:

$a = \dfrac{kx}{m_1 + m_2} - g \sin\theta$

For block $m_2$, the forces acting along the incline are the normal force $N$ exerted by $m_1$ and the component of gravity $m_2 g \sin\theta$.

The equation of motion for $m_2$ is:

$N - m_2 g \sin\theta = m_2 a$

Substituting the value of $a$:

$N = m_2 (a + g \sin\theta) = m_2 \left( \dfrac{kx}{m_1 + m_2} - g \sin\theta + g \sin\theta \right) = \dfrac{m_2 kx}{m_1 + m_2}$

The blocks separate when the normal force $N$ becomes zero.

$N = 0 \Rightarrow \dfrac{m_2 kx}{m_1 + m_2} = 0 \Rightarrow x = 0$

This means the blocks separate when the spring acquires its natural length.