Simple Harmonic Motion (SHM)

Introduction

• What is Simple Harmonic Motion?
  • Behavior of a particle in terms of velocity, acceleration
  • Applications of Simple Harmonic Motion

Simple Pendulum

• Mean Position: The particle remains stationary
• Oscillatory Motion: Repetitive motion of the particle
• Difference between Periodic Motion and Simple Harmonic Motion
• Periodic Motion repeats over time but doesn't require movement to mean position

Periodic Motion vs Simple Harmonic Motion

• All simple harmonic motions are periodic, but not all periodic motions are simple harmonic
• Discussion about phase differences and graphs

Mathematical Formulas (Graphs)

• Displacement: y = a sin (ωt)
• Velocity: v = aω cos (ωt)
• Acceleration: a = -ω² y
• Phase differences (Displacement, Velocity, Acceleration)

Experiment: Spring Mass System

• Spring Constant: F = -kx
• Time Period: T = 2π√(m/k)

Graphs and Analysis

• y vs t Graph: Sine wave
• v vs t, and a critical details
• Position in maximum and minimum conditions

Springs Series and Parallel Combination

• Series: k_eq = (k1 * k2) / (k1 + k2), T = 2π√(m/k_eq)
• Parallel: k_eq = k1 + k2, T = 2π√(m/k_eq)
• Applications and Problems

Increasing Mass and System Behavior

• Effects of mass changes on time period

What is Damping? Critical and Small Reference

• Suggested experiments for direct explanation
• Example of mass and spring system. No load and interaction explanations

Revision Points and Clarifications with Each Question

• Careful problem solving on exercise equations - key references

Conclusion

• Understanding the theory of Simple Harmonic Motion is important
• Practice and understanding the manner of motion and acceleration.