The correct statement for a simple harmonic oscillator is option 2: the force acting on the oscillator is directly proportional to the displacement from the mean position and is in the opposite direction.

In a simple harmonic oscillator, the oscillator moves back and forth around its equilibrium position in a periodic manner. The force acting on the oscillator is directly proportional to the displacement from the mean position. This means that as the oscillator moves further away from its equilibrium position, the force on the oscillator increases, and as it gets closer to the equilibrium position, the force decreases. The direction of the force is always opposite to the displacement from the equilibrium position.

The statement in option 1 is incorrect because the force is in the opposite direction, not the same direction.

For option 3, the acceleration of the oscillator is not constant. It changes over time as the oscillator moves back and forth.

Option 4 is also incorrect as the velocity of the oscillator is periodic in a simple harmonic motion. It oscillates between positive and negative velocities as the oscillator moves back and forth.