Problem Statement:
Two blocks A and B of masses m and 2m respectively are held at rest such that the spring is in its natural length. We need to determine the acceleration of both blocks just after they are released.

Solution:
1. Free Body Diagram:
Let's begin by drawing the free body diagram for each block:

Block A:
- Weight (mg) acting downwards.
- Tension force (T) acting to the right.
- Force exerted by the spring (Fs) acting to the left.

Block B:
- Weight (2mg) acting downwards.
- Force exerted by the spring (Fs) acting to the left.

2. Forces and Acceleration:
According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration. Using this principle, we can write the equations of motion for each block:

Block A:
- Net force = ma
- T - Fs = ma

Block B:
- Net force = ma
- Fs = 2ma

3. Spring Force:
The force exerted by the spring is given by Hooke's law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. Mathematically, this can be expressed as:

Fs = -kx

Where Fs is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

4. Equilibrium Position:
Since the blocks are initially held at rest, the spring is in its natural length, which means there is no displacement (x = 0) and no force exerted by the spring (Fs = 0).

5. Solving the Equations:
Using the information from step 4, we can substitute Fs = 0 in the equations of motion for both blocks:

Block A:
- T - 0 = ma
- T = ma

Block B:
- 0 = 2ma
- 0 = 2a

6. Acceleration:
From the equations in step 5, we can conclude that the acceleration of block B is zero (a = 0). This means that block B remains at rest throughout the motion.

For block A, the acceleration (a) is equal to the tension force (T) divided by the mass (m). Therefore, the acceleration of block A is T/m.

7. Conclusion:
After releasing the blocks, block A will experience an acceleration equal to the tension force divided by its mass, while block B remains at rest. The exact value of the acceleration depends on the specific values of mass and tension force.