04/06/2026
Title: How Simple Harmonic Motion Comes From Circular Motion - SS2 Physics
Explanation:
Simple Harmonic Motion, SHM, can be explained using circular motion.
Imagine a ball moving round a circle with constant speed. If we shine light on it and look at its shadow on a straight line, that shadow moves back and forth.
Displacement: The distance of the shadow from the center = x = A cos θ, where A = radius of circle = amplitude.
Condition for SHM: When we check the acceleration of the shadow, we find that
Acceleration = -ω² × displacement
That means the acceleration is always pointing back to the center and is proportional to the displacement. This is the main condition for SHM.
Conclusion: So the to-and-fro motion of the shadow is Simple Harmonic Motion.
The circular motion is called the “reference circle” of the SHM.
Formula to remember: a = -ω²x
Where a = acceleration, ω = angular speed, x = displacement
