The force acting on a particle executing simple harmonic motion is

Simple Harmonic Motion (SHM) is defined by a restoring force that is directly proportional to the displacement of the particle from its equilibrium or mean position [t1][t4]. Mathematically, this is expressed through Hooke's Law as F = -kx, where 'F' is the restoring force, 'k' is the force constant, and 'x' is the displacement [t4][t7]. The negative sign in the equation signifies that the force always acts in the opposite direction of the displacement, meaning it is consistently directed towards the mean position to restore equilibrium [t2][t3]. Consequently, as the particle moves further from the center, the magnitude of the force increases, but its direction remains focused on pulling the particle back to the midpoint [t4][t6]. This specific relationship between force, displacement, and direction is the fundamental requirement for a system to execute SHM [t6].

Sources

1. [1] https://en.wikipedia.org/wiki/Restoring_force