Final answer:
Simple harmonic motion requires an equilibrium position and acceleration that is proportional to and directed towards the displacement from that position. A classic example is a mass on a spring or a small-angle pendulum swing. Option d)Acceleration proportional to displacement is the correct answer.
Step-by-step explanation:
Conditions for Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is proportional to the displacement from its equilibrium position and acts in the opposite direction. For SHM to occur, certain conditions must be met:
- The motion must have an equilibrium position, which is the position where the net force acting on the object is zero.
- Acceleration must be proportional to the displacement from the equilibrium position.
- The direction of acceleration is towards the equilibrium position.
To identify an SHM system, we can consider a classic example of a mass attached to a spring on a frictionless table, or a pendulum with a small swing. The crucial aspect is that the object experiences a restoring force that is directly proportional to its displacement and directs it back towards the equilibrium. For small displacements, where the sine of the angle of displacement equals the angle in radians (which is a good approximation for angles less than about 15°), a pendulum exhibits SHM.
Therefore, the correct option that must be met for producing SHM is d) Acceleration proportional to displacement.