Here's why:
* SHM is defined by a restoring force: This force always acts to bring the oscillating object back to its equilibrium position.
* The force is proportional to displacement: The magnitude of the restoring force is directly proportional to the displacement from equilibrium.
* The perpendicular component of force is responsible for restoring motion: In SHM, the force can be decomposed into two components: one parallel to the direction of motion and one perpendicular to it. The perpendicular component is the restoring force, pulling the object back towards equilibrium.
Example:
Imagine a mass attached to a spring, oscillating horizontally. The restoring force acts along the spring, pulling the mass back towards the center (equilibrium). If you analyze this force, you'll find that the component perpendicular to the motion is the one responsible for changing the direction of the mass, causing it to turn around and move back towards the center.
Key takeaway: In SHM, the perpendicular component of the force is crucial for the oscillatory motion. It acts as a restoring force, ensuring the object oscillates back and forth around its equilibrium position.
