A pendulum undergoes simple harmonic motion. The phase difference between the displacement and the acceleration of the particle is:

Explanation

In a pendulum undergoing simple harmonic motion (SHM), the displacement and the acceleration of the particle are 90 degrees out of phase. This means that when the displacement is at its maximum (either positive or negative), the acceleration is zero. Similarly, when the displacement is at its equilibrium position (zero displacement), the acceleration is at its maximum (either positive or negative).Since the phase difference between the displacement and the acceleration in SHM is π/2 radians or 90 degrees, the correct option is π/2.In simple harmonic motion (SHM), the displacement and acceleration of an object are related by a phase difference of pi (π) radians, or 180 degrees.Mathematically, we can represent SHM asx = A cos(ωt + φ)where:- x is the displacement of the object from its equilibrium position- A is the amplitude of the motion- ω is the angular frequency of the motion- t is the time- φ is the phase angle The velocity and acceleration of the object can be obtained by taking the first and second derivatives of the displacement equation:v = -Aω sin(ωt + φ)a = -Aω^2 cos(ωt + φ)We can see that the displacement and acceleration equations differ by a phase angle of pi (π) radians, as the cos and sin functions have a phase difference of pi/2 radians. Therefore, the phase difference between the displacement and acceleration of an object in SHM is pi radians.