# Lesson Plan: Simple Harmonic Motion
**Educational Level:** Senior Secondary 2
**Subject:** Physics
**Duration:** 60 Minutes
**Topic:** Simple Harmonic Motion (SHM)
**Objectives:**
1. Define Simple Harmonic Motion (SHM).
2. Understand the characteristics of SHM.
3. Derive and explain the equations of SHM.
4. Identify examples of SHM in daily life.
5. Solve problems associated with SHM.
**Materials:**
- Whiteboard and markers
- Projector and laptop
- Slinky or spring
- Pendulum setup
- SHM problem set handouts
- Graph paper
- Scientific calculators
---
**Lesson Outline:**
### Introduction (5 minutes)
**Activity: Brainstorming**
- Ask students if they have heard the term "Simple Harmonic Motion" and what they think it might mean.
- Introduce the topic by linking it to observable phenomena such as swinging pendulums, vibrating strings of musical instruments, and springs.
### Direct Instruction (20 minutes)
**Key Concepts:**
1. **Definition of SHM:**
- Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to displacement.
2. **Characteristics of SHM:**
- Restoring force \( F \) is proportional to displacement \( x \) : \( F = -kx \)
- The motion is sinusoidal in nature and can be described by sine and cosine functions.
- Amplitude, Frequency, and Period:
- **Amplitude (A):** The maximum displacement from equilibrium.
- **Frequency (f):** The number of oscillations per unit time.
- **Period (T):** The time taken for one complete cycle ( \( T = \frac{1}{f} \) ).
3. **Equations of SHM:**
- Displacement: \( x(t) = A \cos(\omega t + \phi) \)
- Velocity: \( v(t) = -A\omega \sin(\omega t + \phi) \)
- Acceleration: \( a(t) = -A\omega^2 \cos(\omega t + \phi) \)
- Where \( \omega \) is the angular frequency.
### Demonstration (10 minutes)
**Activity: Practical Demonstration**
- Demonstrate SHM with a pendulum: Show how the pendulum returns to its equilibrium position and discuss the properties.
- Demonstrate SHM with a slinky or spring: Show how stretching and releasing a spring demonstrates SHM, explaining the forces involved.
### Guided Practice (10 minutes)
**Activity: Interactive Problem Solving**
- Distribute problem sets and work through a sample problem on the board:
```markdown
**Example Problem:**
A mass attached to a spring oscillates with an amplitude of 0.5m and a period of 2 seconds. Determine:
1. The angular frequency (\( \omega \))
2. The maximum velocity (\( v_{\max} \))
3. The time taken to move from the equilibrium position to the maximum displacement.
**Solution:**
1. \( \omega = \frac{2\pi}{T} = \frac{2\pi}{2 \text{s}} = \pi \text{ rad/s} \)
2. \( v_{\max} = A\omega = 0.5 \text{m} \times \pi \text{ rad/s} = 1.57 \text{ m/s} \)
3. For SHM, \( t = \frac{T}{4} = \frac{2 \text{s}}{4} = 0.5 \text{s} \).
```
### Independent Practice (10 minutes)
**Activity: Problem Set Completion**
- Have the students work on the remaining problems individually or in small groups.
- Circulate the room to offer assistance and ensure understanding.
### Closing (5 minutes)
**Activity: Quick Review and Q&A**
- Recap the main points of the lesson: definition, characteristics, equations, and examples of SHM.
- Allow time for students to ask questions.
- Assign homework: Research and describe one real-world example of SHM that was not discussed in class. Explain why it can be considered SHM.
### Homework:
1. Research and write about a real-world application of SHM.
2. Complete additional problem sets if provided.
---
**Assessment:**
- Observe participation and contributions during brainstorming and discussions.
- Review and provide feedback on solved problem sets.
- Assess understanding through homework assignments.
**Differentiation:**
- Provide additional resources or simpler problems for students who need more support.
- Offer more complex problems for students who require further challenges.
**Extensions:**
- Explore damped and forced oscillations in future lessons.
- Connect SHM to waves and sound in upcoming units.
**Notes:**
- Ensure all demonstrations and practical activities are performed safely.
- Reinforce concepts with visual aids and real-life examples to make the topic more relatable.