Displacement in Simple Harmonic Motion

Displacement in the context of oscillatory motion is represented by the variable $x$ .
The equilibrium position of an object, which serves as the central reference point for the motion, is defined as $x = 0\,m$ .
The term "Amplitude," denoted by the symbol $A$ , refers to the maximum displacement of the object from its equilibrium position.
The motion involves oscillation between two extreme points: a positive maximum displacement of $+A$ and a negative maximum displacement (labeled in the material as "-Amplitude") of $-A$ .

Simple Harmonic Motion (SHM) is mathematically modeled using trigonometric functions, specifically sine and cosine.
The selection of either a sine ( $\sin(x)$ ) or a cosine ( $\cos(x)$ ) function to represent the motion depends entirely on the starting position of the SHM at time $t = 0$ .
A primary equation used to describe the displacement over time is: $x = A\cos(2\pi ft)$ .
The choice of utilizing the cosine function in this specific equation is considered arbitrary; the motion can be represented by various trigonometric formulations.
Another valid formulation for the displacement is given as: $X = A\sin(\omega t + )$ .
In these equations, the variable $t$ represents time, and the variable $f$ represents frequency.

The displacement-versus-time graph for an object in SHM is characterized by a specific shape known as "sinusoidal."
The term "sinusoidal" is derived from the fact that the graph mirrors the periodic profile of trigonometric sine or cosine functions.
On the graph, the vertical axis corresponds to displacement ( $x$ ) and the horizontal axis corresponds to time ( $t$ ).
The graph shows the position of the object oscillating continuously between the upper peak of $+A$ and the lower trough of $-A$ .
Visual components of the provided diagram include a "Pen" or recording instrument that traces the sinusoidal path as time progresses.
Annotations such as "AAAA" or "AAAAA" are located near the peaks of the motion's displacement curve.
The material contains a visual representation of the system (indicated by "-eeeeeeeeee," likely signifying a spring mechanism) and includes the numerical reference "10," possibly signifying a page number or section.