Simple Harmonic Motion (SHM)
Kinematic equation a = -ω²x, displacement, velocity, acceleration phase relationships, simple pendulum, helical springs, and conservation of mechanical energy.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Define simple harmonic motion using the restoring acceleration condition a = -ω²x.
- Calculate periodic time, maximum speed, and energy transformations for pendulums and oscillating springs.
Core Theory & Concepts
Simple Harmonic Motion (SHM) is the fundamental oscillatory model in physics. Any system experiencing a linear restoring force proportional to displacement executes SHM, forming the theoretical basis of mechanical vibrations, acoustic resonators, and electromagnetic wave transmitters.
Defining Equation of SHM
An oscillation is simple harmonic if its acceleration is directly proportional to displacement from equilibrium and always directed towards equilibrium: a = -ω² x.
Energy Conservation in SHM
Total mechanical energy is constant: E = KE + PE = 1/2 m ω² (A² - x²) + 1/2 m ω² x² = 1/2 m ω² A².
Common Misconceptions
Believing velocity and acceleration are maximum at the same instant.
Syllabus Topic Outline
- 1Definition and characteristic equation of SHM (a = -ω²x)
- 2Kinematic relationships: x(t), v(t), and a(t) phasor diagrams
- 3Total mechanical energy in SHM: kinetic and potential interchange
- 4Simple pendulum and loaded helical spring period derivations