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

Mastering Energy Equations in Harmonic Oscillators

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

Table of content

Energy transfer in simple harmonic motion (SHM)

🤓 Basics

  • SHM involves the transfer of energy between potential (Ep) and kinetic (Ek).

💡 Real-world Example: Imagine a swinging pendulum. At its highest point, it has maximum potential energy but zero kinetic energy. As it swings down, potential energy gets converted to kinetic energy.

 

🧮 Kinetic Energy (Ek)

  • Formula: Ek=\(\frac 12\)​mv2
  • For SHM: v= ω2(x0− x2) Thus, Ek=\(\frac 12\)​mω2(x02−x2)

 

🧮 Potential Energy (Ep)

  • Formula: Ep=Etot−Ek
  • After a bit of math: Ep =\(\frac 12\)​mω2x2

 

🔍 Total Energy (Etot)

  • When the object is moving the fastest (x=0),

Etot = \(\frac 12\)​mω2x02

 

📊 Graphical Insights

  • The graphs for Ek and Ep vs. displacement are shaped like parabolas.
  • The point where Ek = Ep isn't at half the amplitude but closer to x0 (amplitude) from the equilibrium.

💡 Real-world Example: Think of a roller coaster. The potential energy is maximum at the top, and as it descends, kinetic energy increases. The shapes of these energy curves would be parabolic!

Worked example - SHM energy

(Refer to the given graph for visual representation.)

  • Amplitude of motion: 20 cm a. Total energy = 8.0 J b. When Ek = Ep - Displacement is approximately ±14 cm. c. Ek vs. displacement: Inverted parabolic shape compared to the Ep graph. d. Maximum speed = 2.5 m/s e. Oscillation period = 0.51 s

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IB Resources
Theme C - Wave Behaviour
Physics SL
Physics SL

Theme C - Wave Behaviour

Mastering Energy Equations in Harmonic Oscillators

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

Table of content

Energy transfer in simple harmonic motion (SHM)

🤓 Basics

  • SHM involves the transfer of energy between potential (Ep) and kinetic (Ek).

💡 Real-world Example: Imagine a swinging pendulum. At its highest point, it has maximum potential energy but zero kinetic energy. As it swings down, potential energy gets converted to kinetic energy.

 

🧮 Kinetic Energy (Ek)

  • Formula: Ek=\(\frac 12\)​mv2
  • For SHM: v= ω2(x0− x2) Thus, Ek=\(\frac 12\)​mω2(x02−x2)

 

🧮 Potential Energy (Ep)

  • Formula: Ep=Etot−Ek
  • After a bit of math: Ep =\(\frac 12\)​mω2x2

 

🔍 Total Energy (Etot)

  • When the object is moving the fastest (x=0),

Etot = \(\frac 12\)​mω2x02

 

📊 Graphical Insights

  • The graphs for Ek and Ep vs. displacement are shaped like parabolas.
  • The point where Ek = Ep isn't at half the amplitude but closer to x0 (amplitude) from the equilibrium.

💡 Real-world Example: Think of a roller coaster. The potential energy is maximum at the top, and as it descends, kinetic energy increases. The shapes of these energy curves would be parabolic!

Worked example - SHM energy

(Refer to the given graph for visual representation.)

  • Amplitude of motion: 20 cm a. Total energy = 8.0 J b. When Ek = Ep - Displacement is approximately ±14 cm. c. Ek vs. displacement: Inverted parabolic shape compared to the Ep graph. d. Maximum speed = 2.5 m/s e. Oscillation period = 0.51 s

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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