In a mass-spring system with no friction, the force of the spring (Fs) is not constant, and the acceleration of the mass (m) is not constant either.
The force exerted by a spring can be given by Hooke's Law:
Fs = -kx
where Fs is the force of the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position.
As the mass oscillates back and forth, its displacement from the equilibrium position changes continuously. Therefore, the force exerted by the spring, which is directly proportional to the displacement, also changes throughout the oscillation. At maximum displacement (maximum compression or extension), the force of the spring is at its maximum. At the equilibrium position, the force of the spring is zero.
Since the force of the spring is not constant, the acceleration of the mass is also not constant. The acceleration of the mass is given by Newton's second law:
F = ma
where F is the net force acting on the mass and a is its acceleration. In the case of a mass-spring system, the net force is the sum of the force of the spring and any external forces. As the displacement and force of the spring change, the net force acting on the mass also changes, resulting in a varying acceleration.
During the oscillation, the mass-spring system experiences simple harmonic motion, where the acceleration and force of the spring continuously change in magnitude and direction, but they always remain proportional to each other.