Simple Harmonic Motion

Content Standards

In this lesson, the learner will understand the concept of oscillatory motion and Simple Harmonic Motion (SHM). Explore how the time period of a simple pendulum depends on its length and gravity. Relate theoretical expressions with experimental observations.

Performance Standards

Students will be able to:

Define SHM and its characteristics.
Explain the restoring force in a pendulum and its relation to displacement.
Experiment with pendulum length in a virtual lab and observe changes in time period.
Use the formula T=2π sq rt. (L/g) to calculate time period and compare with simulation.

Alignment Standards

Reference: NCERT Class 6 Science

The lesson is aligned with the NCERT Grade 11 Physics Book-Chapter 13: Oscillations, Section:8 – Simple Harmonic Motion

Learning Objectives

By the end of the lesson, students will be able to:

Define oscillation and SHM.
State the relation between pendulum length and time period.
Verify SHM experimentally through simulation.
Analyze real-life examples of SHM.

Prerequisites (Prior Knowledge)

Students should already know:

Basic concepts of force and Newton’s laws.
Concept of periodic motion.
Acceleration due to gravity (g).

Introduction

In this session,

In this session, students are introduced to Simple Harmonic Motion (SHM) using a simple pendulum. SHM is a type of oscillatory motion where the restoring force is directly proportional to displacement and directed towards equilibrium.The activity focuses on how the length of the pendulum and gravity affects its time period, reinforcing the formula T=2π sq rt.(L/g).

Timeline (40 Minutes)

Title	Approximate Duration	Procedure	Reference Material
Engage	5	Teacher demonstrates a pendulum Ask: “What do you think will happen if we increase the length of this pendulum?”	Slides
Explore	10	Students use the Virtual Lab (SHM Pendulum) to change pendulum length and observe time period & oscillation speed.	Virtual lab
Explain	10	The teacher explains SHM: restoring force, displacement, time period formula. Relate simulation results to theory.	Slides + Virtual Lab
Evaluate	10	Students will attempt the Self Evaluation task on LMS	Virtual Lab
Extend	5	Students brainstorm SHM examples: swings, springs, guitar strings, oscillations in molecules.	Slides

Simple Harmonic Motion

Introduction

Simple Harmonic Motion (SHM) is a special type of oscillatory motion where a particle moves back and forth about a mean position under the influence of a restoring force. The restoring force is directly proportional to the displacement and always directed towards the mean position.

In this activity, students study SHM through a simple pendulum in a virtual lab. By changing the length of the pendulum and value for gravitational acceleration, they observe how the time period of oscillation changes, and they compare their results with the theoretical formula.

Theory

A pendulum consists of a small bob suspended by a light, inextensible string. When displaced from its equilibrium position and released, it oscillates to and fro under the influence of gravity.

The motion of the pendulum is approximately Simple Harmonic Motion (for small angular displacements)
The restoring force acting on the pendulum bob is proportional to the displacement from the mean position.
The time period (T) of a simple pendulum is given by:

T=2𝜋√(L/g)

Where:

T = Time period (s)
L = Length of pendulum (m)
g = Acceleration due to gravity (9.8 m/s² on Earth)

Key Points:

Time period is independent of mass of the bob/pendulum ball.
Time period increases as length increases.
The frequency of oscillation decreases with increase in length.

Applications of SHM:

Pendulum clocks
Seismographs
Musical instruments (strings, tuning forks)
Study of molecular vibrations

Vocabulary

This is the list of vocabulary terms used throughout the lesson.

Oscillation
Simple Harmonic Motion (SHM)
Restoring Force
Amplitude
Time Period (T)
Frequency (f)
Phase
Pendulum Equilibrium Position –
Damping

Simple Harmonic Motion

Introduction

Welcome to the Virtual Lab on Simple Harmonic Motion (SHM)!

In this lab, you will explore how objects move back and forth in a regular repeating manner, just like a swing or a vibrating string. This type of motion is called Simple Harmonic Motion. It is an important concept in physics because it helps us understand the behavior of oscillations in everyday life and in scientific applications such as pendulums, springs, musical instruments, and even waves.

Through this VR experience, you will observe how the displacement of an object changes during SHM. You will also see how factors like mass, length, and restoring force affect the time period and frequency of oscillations.

This interactive lab will make it easier for you to visualize the motion in 3D, experiment with different conditions, and connect the theory of SHM to real-life phenomena.

Key Features

Interactive 3D simulation of a simple pendulum

Adjustable pendulum length (L) and gravity (g)

Automatic calculation of time period (T)

Option to compare experimental and theoretical values

Integrated MCQs and reflection prompts at the end
MCQs are integrated at the end of each module for engagement.

Step-by-Step Procedure for VR Experience

Step 1: Instructions

Launch the SHM Pendulum simulation.
Observe the pendulum setup (a bob suspended from a string).
Use on-screen controls to adjust pendulum length (L) and gravitational acceleration (g).
Start the simulation and watch the pendulum oscillate.

Step 2: Formula & Explanation

Recall that for small oscillations, the motion is Simple Harmonic Motion (SHM).
Restoring force is directly proportional to displacement and directed toward equilibrium.
To Remember-

T increases with L; T decreases with higher g; Mass of the bob does not affect the time period.

Step 3: Vary L and g to Calculate Time

Play with the parameters of L and g to see how it affects the Time period.

Step 4: Evaluation

After interaction, students proceed to the quiz:
- 2 MCQs