C.1.7—Qualitative energy changes in SHM
- Syllabus
- First assessment 2025
- Objective
- —
- Level
- HL
Track SHM Energy Through One Cycle
Describe one complete cycle
In ideal SHM, total mechanical energy is constant. As the particle moves from an extreme position to equilibrium, stored potential energy changes into kinetic energy; from equilibrium to the opposite extreme, kinetic energy changes back into potential energy.
Use quarter-cycle checkpoints
At an extreme, speed and kinetic energy are zero while the relevant potential energy is maximum. At equilibrium, speed and kinetic energy are maximum while that potential energy is minimum. The energy pattern repeats every cycle.
Connect the model
A circular-motion picture can help visualize phase: the projected coordinate oscillates between two extremes and passes equilibrium twice per cycle. Use it as a representation of the oscillation, while the energy explanation remains based on the SHM position and speed.
Common trap
Do not claim that the energy transfer stops at equilibrium. The particle has maximum speed there, so the transfer reverses direction as it continues toward the next extreme.
C.1.7 Exam Analysis
This exam question is unavailable.
Retrieve the Core C.1 Simple Harmonic Motion Model
Recognize SHM
SHM requires a restoring acceleration a=−ω2x about equilibrium. Track displacement, amplitude, period, frequency and angular frequency with T=1/f=2π/ω.
Track one cycle
At an extreme, potential energy is maximum and kinetic energy is zero; at equilibrium, kinetic energy is maximum and potential energy is minimum. Total energy remains constant in ideal SHM.
Read the motion
The gradient of a displacement–time graph is velocity. Acceleration is opposite to displacement. Use the sign of displacement and the gradient to identify direction at any instant.
Final check
Measure displacement from equilibrium, keep amplitude distinct from peak-to-peak distance, and name the relevant potential-energy form for the oscillator.