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Last updated:

November 28, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems.

Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange’s equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

Course Curriculum

    • Newton’s Laws, Cartesian and Polar Coordinates, Dynamics of a Single Particle Unlimited
    • Work-Energy Principle Unlimited
    • Dynamics of a Single Particle: Angular Momentum Unlimited
    • Systems of Particles: Angular Momentum and Work-Energy Principle Unlimited
    • Systems of Particles: Example 1: Linear Momentum and Conservation of Energy, Example 2: Angular Momentum Unlimited
    • Collisions Unlimited
    • 2D-Motion of Rigid Bodies: Kinematics Unlimited
    • 2D-Motion of Rigid Bodies: Kinematics – Instant Centers; Kinetics Unlimited
    • 2D-Motion of Rigid Bodies: Kinetics, Parallel Axis Theorem Unlimited
    • 2D-Motion of Rigid Bodies: Falling Stick Example, Work-Energy Principle Unlimited
    • 2D-Motion of Rigid Bodies: Finding Moments of Inertia, Rolling Cylinder with Hole Example Unlimited
    • 2D-Motion of Rigid Bodies: Rolling Cylinder and Rocker Examples Unlimited
    • Lagrangian Dynamics: Generalized Coordinates and Forces Unlimited
    • Lagrangian Dynamics: Virtual Work and Generalized Forces Unlimited
    • Lagrangian Dynamics: Derivations of Lagrange’s Equations and Examples Unlimited
    • Lagrangian Dynamics: Examples Unlimited
    • Lagrangian Dynamics: Examples and Equilibrium Analysis Unlimited
    • Lagrangian Dynamics: Examples and Equilibrium Analysis (cont.) Unlimited
    • Lagrangian Dynamics: Examples and Equilibrium Analysis (cont.) Unlimited
    • Vibrations: Second Order Systems with One Degree of Freedom – Free Response Unlimited
    • Vibrations: Second Order Systems with One Degree of Freedom – Forced Response Unlimited
    • Vibrations: Free Response of Multi-Degree-of-Freedom Systems Unlimited
    • Vibrations: Two Degrees of Freedom Systems – Wilberforce Pendulum Unlimited
    • Vibrations: Forced Response of Multi-Degree-of-Freedom Systems Unlimited

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Massachusetts Institute of Technology