The phase difference between displacement and acceleration of a particle in a simple harmonic motion i

In a simple harmonic motion, the displacement (x) and acceleration (a) of a particle are related by the equation a = -ω²x, where ω is the angular frequency of the motion.

This equation tells us that the acceleration of the particle is always directed towards the equilibrium position and its magnitude is proportional to the displacement from the equilibrium position.

The negative sign indicates that the acceleration is always in the opposite direction to the displacement.

This means that when the particle is at the maximum displacement (either positive or negative), the acceleration is at its maximum (but in the opposite direction).

On the other hand, when the particle is at the equilibrium position (displacement is zero), the acceleration is also zero.

Therefore, the phase difference between displacement and acceleration in a simple harmonic motion is 180 degrees or π radians. This is because they are always in opposite directions.