Understanding Simple Harmonic Motion (SHM)

Simple Harmonic Motion, or SHM, is a type of movement that repeats over time. You can see this motion best through three main types of graphs: position, velocity, and acceleration. Each graph looks different and is affected by three key factors: amplitude, frequency, and phase. Let’s break down how these factors change the graphs.

1. Amplitude

Amplitude is the biggest distance the object moves from its resting position.

• When the amplitude is larger, the graphs look "taller."
• Position graph: This graph's highest points will be at the amplitude ($A$) and the lowest at ($-A$).
• Velocity graph: A larger amplitude means the highest and lowest speeds go up, showing the object moves faster at the resting point.
• Acceleration graph: Similar to the position graph, the highest points will also be greater since acceleration is linked to the distance from the resting point.

2. Frequency

Frequency tells us how often the motion happens in a certain amount of time.

• If the frequency is higher, the graphs will look more "squished."
• Position graph: A higher frequency means you see more waves in the same amount of time.
• Velocity graph: More frequent waves show that the speed is changing faster.
• Acceleration graph: Like velocity, a higher frequency means quicker changes in acceleration as well.

3. Phase Angle

The phase angle changes where the motion starts. If the phase angle changes, the whole graph will shift left or right.

• Position graph: A change in phase means the object begins in a different spot.
• Velocity and acceleration graphs: These graphs will also move horizontally, but their shape will still look the same.

By learning about these three factors—amplitude, frequency, and phase—you can better understand how the graphs of position, velocity, and acceleration in SHM look. This knowledge helps you grasp this important idea in physics!