| Lesson Plan |
| Grade: |
Date: 01/12/2025 |
| Subject: Physics |
| Lesson Topic: use a = –ω2x and recall and use, as a solution to this equation, x = x0 sin ωt |
Learning Objective/s:
- Describe the relationship a = –ω²x and its derivation from Newton’s second law.
- Explain how the sinusoidal solution x = x₀ sin ωt (with φ = 0) represents simple harmonic motion.
- Apply the equations to calculate angular frequency, displacement, and other SHM quantities for mass‑spring systems.
- Analyse common misconceptions about the sign of acceleration and the role of the phase constant.
- Solve a basic SHM problem using the derived formulas.
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Materials Needed:
- Projector and screen
- Whiteboard and markers
- Scientific calculators
- Worksheets with SHM problems
- Spring‑mass apparatus (spring, masses, stand)
- Graphing software (e.g., LoggerPro) for simulations
- Handout of key equations and diagrams
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Introduction:
Begin with a quick demonstration of a spring‑mass system oscillating on the table to capture interest. Ask students what forces are acting and link this to their prior knowledge of Hooke’s law. State that by the end of the lesson they will be able to derive and use a = –ω²x and the solution x = x₀ sin ωt to solve SHM problems.
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Lesson Structure:
- Do‑now (5'): Short quiz on Hooke’s law and basic trigonometry; teacher reviews answers.
- Mini‑lecture (10'): Derive a = –ω²x from F = –kx and Newton’s second law; introduce x = x₀ sin ωt (φ = 0) and discuss sign conventions.
- Guided practice (12'): Work through the example problem (0.5 kg mass, k = 200 N m⁻¹) step‑by‑step, projecting calculations while students follow in their worksheets.
- Interactive simulation (8'): Use graphing software to vary k, m, and x₀, observing changes in ω and the displacement curve.
- Concept check (5'): Exit ticket – write the expression for ω in terms of k and m and explain why acceleration opposes displacement.
- Summary & homework briefing (5'): Recap key formulas, assign additional SHM problems for practice.
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Conclusion:
Summarise the link between the restoring force, the differential equation a = –ω²x, and its sinusoidal solution. Collect the exit tickets to gauge understanding, and remind students to complete the worksheet for homework, focusing on identifying ω and predicting displacement for new mass‑spring scenarios.
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