AP Physics 1 Unit Plan-Simple Harmonic Motion

Unit Title: Simple Harmonic Motion

Prerequisite Knowledge

• Basic concepts of oscillations
• Newton's Laws of Motion
• Energy conservation principles

Unit Objectives

By the end of this unit, students should be able to:

1. Define simple harmonic motion (SHM) and identify its characteristics.
2. Derive and apply the equations of motion for SHM.
3. Analyze the energy transformations in SHM.
4. Understand the relationship between SHM and circular motion.
5. Solve problems involving pendulums and mass-spring systems.
6. Explore real-world applications of SHM.

Unit Duration

• 2 weeks

Key Concepts

1. Simple Harmonic Motion (SHM)

   • Definition and characteristics
   • Restoring force and equilibrium position

2. Equations of Motion for SHM

   • Displacement: $x(t)=A\cos (\omega t+\varphi )$
   • Velocity and acceleration in SHM

3. Energy in SHM

   • Potential and kinetic energy
   • Total mechanical energy conservation

4. SHM and Circular Motion

   • Connection between SHM and uniform circular motion
   • Phase relationships

5. Pendulums and Mass-Spring Systems

   • Derivation of period and frequency
   • Factors affecting period

Lesson Breakdown

Lesson 1: Introduction to SHM

• Objective: Define SHM and identify its characteristics.
• Activities:
  • Demonstration: Mass-spring system and pendulum.
  • Discussion on restoring forces and equilibrium.
• Homework: Basic problems on identifying SHM.

Lesson 2: Equations of Motion for SHM

• Objective: Derive and apply equations of motion for SHM.
• Activities:
  • Derive displacement, velocity, and acceleration equations.
  • Practice problems on SHM equations.
• Homework: Problems on SHM equations.

Lesson 3: Energy in SHM

• Objective: Analyze energy transformations in SHM.
• Activities:
  • Discuss potential and kinetic energy in SHM.
  • Lab: Measure energy changes in a mass-spring system.
• Homework: Problems on energy in SHM.

Lesson 4: SHM and Circular Motion

• Objective: Understand the relationship between SHM and circular motion.
• Activities:
  • Explore phase relationships and circular motion analogy.
  • Visual demonstration using a rotating platform.
• Homework: Problems on SHM and circular motion.

Lesson 5: Pendulums and Mass-Spring Systems

• Objective: Solve problems involving pendulums and mass-spring systems.
• Activities:
  • Derive period and frequency for pendulums and springs.
  • Lab: Investigate factors affecting period.
• Homework: Problems on pendulums and mass-spring systems.

Lesson 6: Review and Practice

• Objective: Consolidate understanding and prepare for assessment.
• Activities:
  • Group problem-solving: Mixed SHM problems.
  • AP-style multiple-choice and free-response questions.
  • Review key concepts of SHM.

Assessments

• Formative Assessments:

  • Quizzes on key concepts.
  • Lab reports and reflections.

• Summative Assessments:

  • Unit test covering all key concepts.
  • Project presentation on a real-world application of SHM.

Resources

• Textbook: AP Physics 1 textbook chapters on oscillations and SHM.
• Online simulations (e.g., PhET Interactive Simulations).