Study Notes
In simple harmonic motion (SHM), energy continuously shifts between kinetic and potential forms, while the total energy remains constant. The speed and acceleration of an oscillator vary with displacement, and these relationships can be represented graphically.
- Acceleration — The rate of change of velocity with respect to time. Example: In SHM, acceleration is maximal at the amplitude and is given by a = -ω²x.
- Displacement — The distance from the equilibrium position in a specific direction. Example: Displacement in SHM can be described by x = x₀ sin(ωt) or x = x₀ cos(ωt).
- Kinetic Energy — The energy possessed by an object due to its motion. Example: In SHM, kinetic energy is maximum at the equilibrium position.
- Potential Energy — The energy stored due to an object's position or configuration. Example: Potential energy is maximum at the maximum displacement in SHM.
Exam Tips
Key Definitions to Remember
- Acceleration in SHM: a = -ω²x
- Displacement equations: x = x₀ sin(ωt) or x = x₀ cos(ωt)
- Kinetic Energy: KE = ½ mv²
Common Confusions
- Mixing up when to use sine or cosine for displacement equations
- Confusing the phase difference between displacement, velocity, and acceleration graphs
Typical Exam Questions
- What is the maximum kinetic energy in SHM? It occurs at the equilibrium position.
- How does potential energy vary with displacement in SHM? It is maximum at maximum displacement and zero at equilibrium.
- How do you calculate the total energy of a simple harmonic system? E = ½ mω²x₀²
What Examiners Usually Test
- Understanding of energy exchange between kinetic and potential forms
- Ability to interpret SHM graphs and identify phase differences
- Calculating speed and acceleration at different points in SHM