Final answer:
A particle experiences simple harmonic motion when it is subjected to a force proportional to its displacement from an equilibrium position, in accordance with Hooke's law, without energy loss (assuming no damping). Option C is the correct answer.
Step-by-step explanation:
A particle undergoes simple harmonic motion (SHM) when it experiences a restoring force proportional to its displacement from an equilibrium position. In the context of SHM, the object oscillates back and forth around this equilibrium position without losing energy over time, assuming no damping forces are present.
Hooke's law describes the restoring force for such systems, stating that the force exerted by a spring is directly proportional to the distance the spring is stretched or compressed from its relaxed position. Hence, according to Hooke's law, SHM can occur in a system where the net force on the mass is described by this proportionality to displacement. Additionally, this force acts in the opposite direction of the displacement.
Regarding the distance moved by a particle in a simple harmonic motion in one time period, it covers twice the amplitude during a complete cycle. The amplitude, represented by A, is the maximum displacement from equilibrium, so the particle moves from x = A to x = -A and back to x = A again, covering a distance of 2A. Therefore, option B from the provided information is correct.
In conclusion, the correct answer to the original question is C. force proportional to its displacement from an equilibrium position.