Vibrations – Definition of Amplitude in Oscillatory Motion The maximum displacement of a vibrating body from its mean (equilibrium) position is called the amplitude. Is this definition correct?

Introduction / Context:
When describing oscillations—whether mechanical (springs), structural (beams), or electrical (AC signals)—we routinely use the term amplitude. A precise definition helps prevent confusion in analysis and communication.

Given Data / Assumptions:

• Periodic motion about a mean (equilibrium) position.
• Displacement measured along a defined axis.
• No restriction on the nature of oscillation other than being measurable relative to an equilibrium.

Concept / Approach:
Amplitude A is defined as the maximum absolute displacement from the mean position achieved during oscillation. For SHM, x(t) = A cos(ω t + φ), the amplitude is the constant A, representing the peak magnitude. This definition does not require damping, circular motion, or large angles.

Step-by-Step Solution:
Identify equilibrium position where net restoring force is zero. Track displacement x(t) over time. Determine the maximum absolute value reached: A = max|x(t)|. This maximum is the amplitude by definition.

Verification / Alternative check:
For SHM, differentiate x(t) to find turning points where velocity v = 0; the corresponding x values are ±A. These are the amplitude limits irrespective of damping presence (though for damping the amplitude decays over time).

Why Other Options Are Wrong:
Restricting amplitude to special cases (circular motion, large oscillations, damping) is unnecessary; the definition is general. “Incorrect” contradicts widely accepted terminology in physics and engineering.

Common Pitfalls:
Confusing amplitude with instantaneous displacement at a given time. In damped systems, forgetting that amplitude can be time-varying (envelope), but the definition per cycle remains maximum absolute displacement.

Final Answer:
Correct