Physics of Oscillations and Waves

Oscillations are repeated movements back and forth around an equilibrium point, like a swinging pendulum. Waves occur when these oscillations propagate through space, as in sound or light. In Hamiltonian mechanics, a framework for understanding dynamics, we describe systems using energy rather than forces. This approach analyzes how energy is distributed and conserved during oscillations and wave motion, providing insights into stability and behavior. The Hamiltonian formalism reveals connections between different physical systems, showing that oscillatory phenomena are fundamental to understanding a wide range of physical processes, from simple springs to complex quantum systems.