• Phase Angle (ϕ): Represents any starting point in SHM. Considered as a 'time shift' or 'offset' from the standard sine function.
• Formula:x = x 0 ​sin (ωt+\ϕ)

Where

• 0x0​ is the maximum displacement (amplitude).
• ω is the angular frequency.
• t is time.
• \ϕ is the phase angle.

Fun Fact: Imagine you and a friend are on swings. If both of you start swinging at the same time and at the same speed, there’s no phase difference. But if one of you starts a little late, then there's a time shift or phase angle!

• Displacement-time graphs show how the displacement of an object varies with time.
• Blue Curve in Figure 16 starts from 0 displacement, while Red Curve is about to reach its max. This means the red curve is leading the blue curve.

Real-world example: Imagine two racers on a circular track. If one racer starts a bit ahead of the other, there is a phase difference between them. This phase difference is like the lead the red curve has over the blue.

Defining Equation for SHM:
a = − ω²x Where a is acceleration and ω is angular frequency.

This equation in differential form:
\(\frac {d^2x}{dt^2}\)​ = − ω²x

Did you know?: This equation is a type of second-order differential equation. These equations can be solved by calculus, spreadsheets, or special modeling software. If math is your thing, this equation is a superstar in the IB Diploma programme!