Vibratory mechanics: course overview

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Related lectures (52)

Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.

Forced Harmonic Oscillator

Explores the forced and damped harmonic oscillator, focusing on resonance and initial conditions.

Signal Representation: Fourier Transforms

Covers the representation of signals using Fourier transforms and the properties of signal vectors.

Continuous-time signal processing: Analog LTI filters

Covers the basics of continuous-time signal processing and Fourier analysis in both continuous and discrete time domains.

Forced Harmonic Oscillator: Resonance

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

Vibratory Mechanics: QCMs Week 12 Log in to Mediaspace to watch this video

Covers topics related to vibratory mechanics, including free and forced oscillations.

Fourier transforms: Light-matter interaction Log in to Mediaspace to watch this video

Explores Fourier and Laplace transforms in materials science, focusing on light-matter interaction, diffraction patterns, and crystal properties.

Forced Vibrations: Fourier Series and Periodic Steady State Log in to Mediaspace to watch this video

Explores force decomposition, Fourier series, and periodic steady state in forced vibrations.

Fourier Series and Laplace Transform Log in to Mediaspace to watch this video

Covers Fourier series calculations and Laplace transform applications for periodic functions efficiently using tables and properties.

Poisson Problem: Fourier Transform Approach Log in to Mediaspace to watch this video

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Introduction to Vibratory Mechanics Log in to Mediaspace to watch this video

Covers basic definitions and transformations in vibratory mechanics.

Fourier Analysis: Inversion Formula Log in to Mediaspace to watch this video

Explores the Fourier inversion formula and the importance of the integral on the half-circle being zero for the method to work.

Fourier Transform: Derivatives and Laplace Transform Log in to Mediaspace to watch this video

Explores the Fourier transform properties with derivatives and introduces the Laplace transform for signal transformation and solving differential equations.

Signals, Instruments, and Systems: System Properties and Transforms Log in to Mediaspace to watch this video

Introduces system properties, Laplace Transform, and analog filters for signal analysis.

Structures: Vibrations and Miles' Formula Log in to Mediaspace to watch this video

Covers the assembly of structures, vibrations, and Miles' Formula for estimating loads due to random vibrations.

Introduction to the z-Transform Log in to Mediaspace to watch this video

Covers the z-Transform, LTI systems, and signal processing applications.

Introduction to the Laplace Transform Log in to Mediaspace to watch this video

Covers the Laplace Transform, LTI systems, Fourier Transforms, and properties.

Frequency Response of LTI Systems Log in to Mediaspace to watch this video

Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.

Convergence of Fourier Series Log in to Mediaspace to watch this video

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Stokes first problem: hydrodynamic separation of variables Log in to Mediaspace to watch this video

Explores the application of separation of variables in hydrodynamics and the concept of self-similarity.

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