Lectures related to One-Dimensional Harmonic Oscillator

Path Integral Representation of Propagators

Covers the path integral representation of propagators for free particles and harmonic oscillators.

Explores free undamped oscillations in a harmonic oscillator and their graphical representation over time.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Forced Harmonic Oscillator: Resonance

Explores the forced harmonic oscillator, damping, and resonance phenomenon, focusing on the amplitude of oscillations in resonance.

Hamiltonian Formalism: Conservation Laws

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Circular Motion and Harmonic Oscillator

Explores circular motion, harmonic oscillators, and double springs, elucidating the physics principles behind them.

Ordinary Differential Equations: Second Order

Explores the resolution of second-order linear ODEs with constant coefficients and various source terms.

Ordinary Differential Equations: Second Order Linear Inhomogeneous

Covers the resolution of second-order linear ordinary differential equations with constant coefficients and a source term.

Differential Equations in Physics

Covers ordinary linear homogeneous differential equations, focusing on the harmonic oscillator equation and its solutions.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

One Dimensional Harmonic Oscillator Log in to Mediaspace to watch this video

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Differential Equations: Speed Variation Analysis Log in to Mediaspace to watch this video

Covers the analysis of speed variation using differential equations and small time intervals.

Material Point Model: Basics Log in to Mediaspace to watch this video

Covers the material point model, initial conditions, and Newton's laws in physics.

Numerical Analysis: Stability in ODEs Log in to Mediaspace to watch this video

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Law of Hooke Applications: Spring Problems Log in to Mediaspace to watch this video

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.

Vertical Metronome: Equilibrium and Stability Log in to Mediaspace to watch this video

Explores equilibrium and stability of a vertical metronome system with springs.

Harmonic Oscillators: Equations, Damping, and Resonance Log in to Mediaspace to watch this video

Explores harmonic oscillators, damping effects, forced oscillations, and resonance phenomena in various systems.

Differential Equations in Motion Log in to Mediaspace to watch this video

Explores differential equations for motion, including critical damping and damped oscillators, with applications in complex numbers and examples of mass-spring systems.

Harmonic Oscillator and Hooke's Law Log in to Mediaspace to watch this video

Explores harmonic oscillators, Hooke's Law, and elasticity in relation to force and spring elongation.