Lesson Plan

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Lesson Plan
Grade: Date: 01/12/2025
Subject: Physics
Lesson Topic: use the equations v = v0 cos ωt and v = ± ω ()xx022−
Learning Objective/s:
  • Describe the relationship between displacement, velocity, and acceleration in simple harmonic motion.
  • Derive and apply the velocity equations v = v₀ cos ωt and v = ± ω√(x₀² − x²) to solve problems.
  • Interpret the physical meaning of each variable and the sign of the velocity expression.
  • Identify and correct common misconceptions about amplitude, phase, and velocity direction in SHM.
Materials Needed:
  • Projector and screen
  • Whiteboard and markers
  • Printed worksheet with example problem
  • Graph paper and calculators
  • Spring‑mass apparatus (optional demonstration)
  • PowerPoint slides summarising derivations
 Introduction:
Begin with a quick demonstration of a mass‑spring system oscillating on a table to capture interest. Review students’ prior knowledge of displacement, amplitude and the basic SHM equations they have already used. Explain that by the end of the lesson they will be able to derive and use two alternative forms of the velocity equation to predict speed at any position. State the success criteria: accurate derivations, correct problem solving, and clear explanation of the sign convention.
Lesson Structure:
  1. Do‑now (5'): Short recall quiz on SHM basics.
  2. Mini‑lecture (10'): Derive v = v₀ cos ωt from x = x₀ sin(ωt + φ) on the board.
  3. Guided practice (10'): Energy‑based derivation of v = ± ω√(x₀² − x²) with class participation.
  4. Example problem (10'): Solve the mass‑spring speed problem together, highlighting sign choice.
  5. Interactive activity (10'): Students sketch x‑t and v‑t graphs on graph paper, marking key points.
  6. Check for understanding (5'): Exit ticket – one sentence explaining when to use each velocity form.
Conclusion:
Summarise that the cosine form links velocity to time while the square‑root form links it directly to displacement, and both arise from the same SHM principles. Ask students to complete an exit ticket describing which form they would choose for a given scenario. Assign homework: two additional SHM problems requiring the use of both velocity equations. Remind them to review the sign convention for direction.