Introduction:
In this problem, we have a mass attached to two springs with different spring constants. The mass is displaced through a small distance and then released. We need to determine the initial acceleration of the mass.

Explanation:
To find the initial acceleration of the mass, we can use Hooke's law which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, this can be expressed as:

F = -kx

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

Step 1: Calculate the total force:
The total force acting on the mass can be calculated by summing up the forces exerted by both springs. Since the displacements of the two springs are in opposite directions (as shown in the figure), the forces exerted by the two springs will have opposite signs.

F_total = -k₁x - k₂x

Step 2: Calculate the net force:
The net force acting on the mass can be calculated by dividing the total force by the mass.

F_net = (F_total) / m

Step 3: Calculate the initial acceleration:
The initial acceleration of the mass can be calculated using Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

a = (F_net) / m

Step 4: Substitute the values:
Now, we can substitute the given values into the equations to find the initial acceleration.

F_total = -(k₁ + k₂)x
F_net = (F_total) / m
a = (F_net) / m

Result:
The initial acceleration of the mass can be calculated by substituting the values of the spring constants and displacement into the equations mentioned above.