Lesson Plan

• Describe how kinetic and potential energy interchange during one cycle of simple harmonic motion.
• Explain why the total mechanical energy of an ideal mass‑spring system remains constant.
• Apply the energy formulas to determine energy distribution at extrema, equilibrium, and halfway points.
• Derive the conservation‑of‑energy relationship using the displacement and velocity expressions for SHM.
• Interpret a labelled diagram to illustrate energy flow in the oscillating system.

• Projector or interactive whiteboard
• Slide deck with equations and a labelled mass‑spring diagram
• Physical mass‑spring apparatus (or a reliable simulation)
• Student worksheets containing the energy‑state table
• Graphing calculators or computers for plotting energy versus time
• Rulers, markers, and graph paper for sketching diagrams

Begin with a short video clip of a bouncing spring to capture interest, then ask students what forms of energy they observe. Review Hooke’s law and the concepts of kinetic and potential energy from previous lessons. State that by the end of the class they will be able to explain how these energies trade places during simple harmonic motion.

1. Do‑now (5 min): Quick quiz on Hooke’s law and basic energy definitions.
2. Mini‑lecture (10 min): Derive \(E_k=\frac12mv^2\) and \(E_p=\frac12kx^2\) for SHM and show that \(E_{total}=\frac12kA^2\) is constant.
3. Demonstration (10 min): Oscillate the mass‑spring system, pause at key positions (extrema, equilibrium, halfway) and discuss the energy state at each.
4. Guided practice (12 min): Students complete the energy‑state table on their worksheets, using the equations provided.
5. Simulation activity (8 min): In pairs, use a web‑based SHM simulator to plot kinetic, potential, and total energy versus time.
6. Check for understanding (5 min): Exit‑ticket question – “At the point where \(x = \pm A/\sqrt{2}\), what fraction of the total energy is kinetic?”

Summarise that energy continuously swaps between kinetic and potential forms while the total remains unchanged, reinforcing the sinusoidal nature of SHM. Collect exit tickets and remind students to finish the worksheet at home, then assign a short problem set requiring them to calculate energy values for a given amplitude and mass.