In simple harmonic motion (SHM), the displacement of an oscillating object from its equilibrium position at a given time is denoted by the variable "x." The amplitude, on the other hand, represents the maximum displacement of the object from its equilibrium position.
While the amplitude is a measure of the maximum extent of the motion, the displacement, "x," varies continuously with time during SHM. It represents the position of the object at any given moment in time relative to its equilibrium position. The displacement can be positive or negative, depending on whether the object is on one side or the other of its equilibrium position.
The reason why the displacement, "x," is not always equal to the amplitude is because the object in SHM does not necessarily start at the extreme positions corresponding to the amplitude. SHM is characterized by the motion of an object back and forth around an equilibrium point, and the object can start its motion from any initial position.
For example, if you consider a pendulum, the amplitude would represent the maximum angle the pendulum swings from its equilibrium position, while the displacement at a particular moment would give the current angle of the pendulum from its equilibrium position.
Therefore, in SHM, the displacement, "x," and the amplitude are distinct quantities. The displacement represents the instantaneous position of the object at any given time, while the amplitude represents the maximum extent of the motion.