Oscillations and simple harmonic motion

Anything that oscillates about a position of equilibrium, provided the push is not too large, behaves like a spring: the restoring force is proportional to the displacement and points in the opposite direction, $F = -Kx$. This is the archetype of simple harmonic motion, which we find again in the mass-spring system, the pendulum, the tuning fork, the molecules of a crystal and $LC$ circuits. This chapter starts from the equation of motion and its sinusoidal solution, moves on to energy and the pendulum, shows that every small oscillation is harmonic, and closes with damping, resonance and coupled oscillators.

Sections

• The ideal spring and the equation of motion
• Energy in the harmonic oscillator
• The simple pendulum
• All small oscillations are harmonic
• Damped oscillations
• Forced oscillations and resonance
• Coupled oscillators: normal modes

Exercises

• All the worked exercises in the chapter