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

Simple Pendulum & Its Harmonic Motion Explained

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

Table of content

Let's swing into the world of pendulums and oscillations!

Simple pendulum 🕰

  • What is it? An object on the end of a string, swinging in a vertical plane.
  • Harmonic Motion? Yep, but the swing angle from vertical should be <10°.
  • String Length: l
  • Mass of Bob: m
  • Swing Angle: θ

Restoring force 📈

  • The force that pulls the pendulum bob back is −mg sin (θ).
    • Why negative? Angle measured anticlockwise, but force acts clockwise!

🔍 Analysis

  • −mgsin(θ) = ma leading to a = − g sin (θ)
  • Length of the arc from equilibrium to bob is x. Thus, θ =\(\frac xl\)
  • So,  a = − \(\frac gl\)​x
    • Fun fact: If θ < 10°, sin (θ) and θ are close (within 1%)!

Period of swing 🧮

  • T=  \(\frac { 2π \sqrt l} g\)

🌊 Similar Analyses: Oscillators like floating cylinders on lakes!

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IB Resources
Theme C - Wave Behaviour
Physics SL
Physics SL

Theme C - Wave Behaviour

Simple Pendulum & Its Harmonic Motion Explained

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

Table of content

Let's swing into the world of pendulums and oscillations!

Simple pendulum 🕰

  • What is it? An object on the end of a string, swinging in a vertical plane.
  • Harmonic Motion? Yep, but the swing angle from vertical should be <10°.
  • String Length: l
  • Mass of Bob: m
  • Swing Angle: θ

Restoring force 📈

  • The force that pulls the pendulum bob back is −mg sin (θ).
    • Why negative? Angle measured anticlockwise, but force acts clockwise!

🔍 Analysis

  • −mgsin(θ) = ma leading to a = − g sin (θ)
  • Length of the arc from equilibrium to bob is x. Thus, θ =\(\frac xl\)
  • So,  a = − \(\frac gl\)​x
    • Fun fact: If θ < 10°, sin (θ) and θ are close (within 1%)!

Period of swing 🧮

  • T=  \(\frac { 2π \sqrt l} g\)

🌊 Similar Analyses: Oscillators like floating cylinders on lakes!

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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