Physics SL
Physics SL
5
Chapters
329
Notes
Theme A - Space, Time & Motion
Theme A - Space, Time & Motion
Theme B - The Particulate Nature Of Matter
Theme B - The Particulate Nature Of Matter
Theme C - Wave Behaviour
Theme C - Wave Behaviour
Theme D - Fields
Theme D - Fields
Theme E - Nuclear & Quantum Physics
Theme E - Nuclear & Quantum Physics
IB Resources
Theme C - Wave Behaviour
Physics SL
Physics SL

Theme C - Wave Behaviour

Unlocking Phase Angle: Dive Into Simple Harmonic Motion

Word Count Emoji
634 words
Reading Time Emoji
4 mins read
Updated at Emoji
Last edited on 5th Nov 2024

Table of content

Basics of phase & phase difference

  • 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!

Interpreting SHM on graphs

  • 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.

The math behind SHM

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!

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IB Resources
Theme C - Wave Behaviour
Physics SL
Physics SL

Theme C - Wave Behaviour

Unlocking Phase Angle: Dive Into Simple Harmonic Motion

Word Count Emoji
634 words
Reading Time Emoji
4 mins read
Updated at Emoji
Last edited on 5th Nov 2024

Table of content

Basics of phase & phase difference

  • 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!

Interpreting SHM on graphs

  • 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.

The math behind SHM

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!

Unlock the Full Content! File Is Locked Emoji

Dive deeper and gain exclusive access to premium files of Physics SL. Subscribe now and get closer to that 45 🌟

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