Displacement and amplitude are related concepts, but they are not always equal. Let's understand the differences between the two:
Displacement: Displacement refers to the distance and direction of an object or particle from its mean or equilibrium position. In simple terms, it measures how far an object is from its starting point. Displacement can be positive, negative, or zero, depending on the direction and magnitude of the object's movement relative to its equilibrium position. Displacement is a vector quantity, meaning it has both magnitude and direction.
Amplitude: Amplitude, on the other hand, specifically refers to the maximum magnitude or distance reached by an oscillating or vibrating object or wave. It represents the maximum extent of the object's motion away from its equilibrium position. Amplitude is a scalar quantity, as it only measures the magnitude of the motion, without considering the direction.
The reason why displacement is not always equal to amplitude is that displacement is influenced by factors such as time and the object's position relative to its equilibrium, while amplitude solely represents the maximum magnitude of the motion. In simple harmonic motion, for instance, an object may oscillate back and forth around its equilibrium position, resulting in a displacement that changes with time. The amplitude in this case represents the maximum distance the object reaches from its equilibrium position, but the actual displacement at any given time may be less than the amplitude.
To summarize, while displacement refers to the object's position relative to its equilibrium, amplitude represents the maximum magnitude or distance of the object's motion. Therefore, displacement and amplitude are related but distinct concepts.