Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)

Term: 3rd Term

Week: 11

Age: 15 years

Duration: 45 minutes

Subject: Physics

Curriculum Theme: Physics

Previous Lesson: Circular Motion.

Topic: SIMPLE HARMONIC MOTION

Subject Matter: Definition of simple harmonic motion, displacement velocity and acceleration in simple harmonic motion, energy of simple harmonic motion, forced vibration, resonance, illustrating SHM using simple pendulum loaded spiral springs and oscillating test tube in liquid.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define Simple Harmonic Motion (SHM).
Describe displacement, velocity, and acceleration in SHM qualitatively.
Explain energy changes during SHM.
Describe forced vibration and resonance.

Affective Domain:

Appreciate the occurrence of SHM, forced vibration, and resonance in everyday situations.
Show interest in observing and understanding periodic motion.

Psychomotor Domain:

Observe and describe periodic motion from demonstrations.
Illustrate SHM using simple pendulum, loaded spiral springs, and an oscillating test tube in liquid.

Collaborate with peers during practical demonstrations.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary Schools.
State Unified Scheme of Work for Physics SSS 1.
New School Physics by M.W. Anyakoha.

Instructional Materials

The teacher will teach this lesson with the aid of:

Simple pendulum setup
Loaded spiral spring
Test tube and liquid container
Stopwatch
Charts on SHM
Worksheets

Rationale for the Lesson

This lesson helps pupils understand a fundamental type of motion that is common in nature and technology. Understanding Simple Harmonic Motion, forced vibration, and resonance enables pupils to explain many everyday phenomena, from the swinging of a clock pendulum to the design of musical instruments and buildings.

Prerequisite/Previous Knowledge

Pupils are expected to have a basic understanding of motion, types of energy (kinetic and potential), and the concepts of oscillation and vibration from previous lessons.

Lesson Content/Board Summary

SIMPLE HARMONIC MOTION (SHM)

Definition of Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction to the displacement. It is an oscillatory motion where the acceleration of the oscillating body is directly proportional to its displacement from the equilibrium position and is always directed towards the equilibrium position.

Examples of Simple Harmonic Motion

The following are common examples of objects exhibiting SHM:

The oscillation of a simple pendulum (for small angles).
The vibration of a loaded spiral spring.
The oscillation of a test tube floating in a liquid.
Vibrating prongs of a tuning fork.

Displacement, Velocity, and Acceleration in SHM

In SHM, these quantities vary sinusoidally with time:

Displacement (x): The distance of the oscillating body from its equilibrium position at any instant. It is maximum at the extremes and zero at the equilibrium position.
Velocity (v): The rate of change of displacement. It is maximum at the equilibrium position and zero at the extreme positions.
Acceleration (a): The rate of change of velocity. It is maximum at the extreme positions (and directed towards equilibrium) and zero at the equilibrium position.

Energy of Simple Harmonic Motion

An object in SHM possesses both kinetic energy (KE) and potential energy (PE). The total mechanical energy (KE + PE) remains constant if there is no damping.

Kinetic Energy: Maximum at the equilibrium position (where velocity is maximum) and zero at the extreme positions (where velocity is zero).
Potential Energy: Maximum at the extreme positions (where displacement is maximum) and zero at the equilibrium position (where displacement is zero).
Energy continuously converts between kinetic and potential energy during the oscillation.

Forced Vibration

Forced vibration occurs when an oscillating system is made to vibrate by an external periodic force. The system is forced to oscillate at the frequency of the external force, which may be different from its natural frequency.

Examples of forced vibration include:

A vibrating tuning fork placed on a table.
The vibration of a car body due to the engine.

Resonance

Resonance is a special case of forced vibration where the frequency of the external force matches the natural frequency of the oscillating system. This leads to a significant increase in the amplitude of oscillation.

Examples of resonance include:

A child on a swing being pushed at the right time (natural frequency).
The breaking of a wine glass by a specific sound frequency.
The tuning of a radio to a particular station.
The collapse of Tacoma Narrows Bridge (due to wind forces matching its natural frequency).

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them to recall different types of motion they have learned (e.g., linear, rotational, oscillatory). The teacher then asks what happens when a suspended pendulum is displaced and released.
Pupils’ Activity: Pupils respond by mentioning types of motion and describing the swinging of a pendulum.
Learning Point: Pupils recall previous knowledge on motion and are introduced to oscillatory motion.

Step 2: Definition of Simple Harmonic Motion

Time: 8 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines Simple Harmonic Motion (SHM) clearly, emphasizing the relationship between restoring force, displacement, and acceleration. The teacher writes the definition on the board.
Pupils’ Activity: Pupils listen attentively, take notes, and ask questions for clarification.
Learning Point: Pupils understand and can define SHM.

Step 3: Illustrating Simple Harmonic Motion

Time: 10 minutes
Teaching Skill: Demonstration/Observation
Teacher’s Activity: The teacher demonstrates SHM using a simple pendulum, a loaded spiral spring, and a test tube oscillating in liquid. The teacher guides pupils to observe the periodic nature of the motion.
Pupils’ Activity: Pupils observe the demonstrations carefully and describe the periodic motion in each setup.
Learning Point: Pupils see practical examples of SHM and can identify characteristics of periodic motion.

Step 4: Displacement, Velocity, and Acceleration in SHM

Time: 7 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains qualitatively how displacement, velocity, and acceleration vary during SHM, highlighting their values at equilibrium and extreme positions. Charts on SHM can be used.
Pupils’ Activity: Pupils listen, observe the charts, and relate the concepts to the demonstrations.
Learning Point: Pupils understand the relationship between displacement, velocity, and acceleration in SHM.

Step 5: Energy of Simple Harmonic Motion

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains the energy transformations (kinetic and potential) that occur during SHM, stating where each type of energy is maximum and minimum.
Pupils’ Activity: Pupils listen and describe the energy changes in SHM.
Learning Point: Pupils understand the energy considerations in SHM.

Step 6: Forced Vibration and Resonance

Time: 5 minutes
Teaching Skill: Explanation/Examples
Teacher’s Activity: The teacher explains forced vibration and resonance, providing clear examples from everyday life and technology to illustrate these phenomena.
Pupils’ Activity: Pupils listen, take notes, and contribute examples of forced vibration and resonance they know.
Learning Point: Pupils can describe forced vibration and resonance and identify their occurrences.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define Simple Harmonic Motion.
Mention two examples of objects that exhibit SHM.
Describe the velocity of an object in SHM at its equilibrium position and at its extreme positions.
Explain what happens to the kinetic and potential energy of an object undergoing SHM as it moves from an extreme position to the equilibrium position.
What is resonance? Give one example.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson and assigns homework from the textbook (e.g., list practical applications of resonance).
Pupils’ Activity: Pupils listen and note the homework.
Learning Point: Pupils review the main concepts of the lesson.

Lesson Keywords

Simple Harmonic Motion (SHM) – A periodic motion where the restoring force is proportional to displacement and acts in the opposite direction.
Oscillation – A repetitive variation of any measure about its equilibrium value.
Displacement – The distance of an oscillating object from its equilibrium position.
Velocity – The rate of change of displacement.
Acceleration – The rate of change of velocity.
Forced Vibration – Vibration caused by an external periodic force.
Resonance – A phenomenon where the frequency of an external force matches the natural frequency of a system, leading to large amplitude oscillations.

Differentiation

For pupils who grasp concepts quickly, the teacher can challenge them to think about the mathematical representation of SHM or to research real-world applications of damping. For pupils needing more support, the teacher can provide simplified diagrams, additional one-on-one explanations during demonstrations, and assign simpler questions from the worksheet.

Note for teachers using this lesson plan

Ensure all demonstration materials are ready and working before the lesson. Allow pupils to actively participate in observations and discussions. Emphasize the qualitative aspects of SHM (displacement, velocity, acceleration, energy) at this level before introducing complex mathematical derivations. Encourage pupils to relate the concepts to their daily experiences to enhance understanding.