In Simple Harmonic Motion (SHM), the acceleration of the object is directly proportional to its displacement from the equilibrium position. However, it acts in the opposite direction.
Key Points:
- Direct Proportionality: This means that as the displacement of the object from its equilibrium position increases, its acceleration also increases. The increase in acceleration is proportional to the displacement.
- Opposite Direction: The crucial aspect is that the acceleration is always directed towards the equilibrium position. This restoring force constantly tries to bring the object back to its rest position.
Mathematical Representation:
This relationship is mathematically expressed as:
a = -ω²x
Where:
- a is the acceleration of the object
- ω is the angular frequency of the motion
- x is the displacement of the object from the equilibrium position
The negative sign in the equation signifies that the acceleration and displacement are always in opposite directions.
In essence, this law defines the characteristic behavior of SHM. It ensures that the motion is oscillatory and that the object continuously moves back and forth around the equilibrium position.