This recitation introduces modal analysis and looks at a double pendulum problem.

Recitation 11: Double Pendulum System

This recitation covers a Lagrange approach  to a problem involving a cart and pendulum.

Recitation 8: Cart and Pendulum, Lagrange Method

This recitation reviews free body diagram strategies, covers equations of motion for multiple degree-of-freedom systems, and addresses a dynamically balanced system.

Recitation 5: Equations of Motion

This recitation covers a direct method of breaking down a problem involving a cart and pendulum.

Recitation 7: Cart and Pendulum, Direct Method

This recitation includes a concept review for the week, problems with the axis of spin on and not on the principal axis, and a discussion on finding the derivative of a rotating vector. The class concludes with a review of the quiz.

Recitation 6: Angular Momentum and Torque

This recitation covers generalized forces in a double pendulum. Questions are also addressed for an upcoming quiz.

Recitation 9: Generalized Forces

This recitation covers a steady state frequency response problem.

Recitation 10: Steady State Dynamics

This recitation takes an in depth look at modal analysis for a double pendulum system.

Recitation 12: Modal Analysis of a Double Pendulum System

This recitation reviews free body diagrams and covers a problem with a torsional spring pendulum followed by a second problem with a rolling pipe on an accelerating truck.

Recitation 4: Free Body Diagrams

This recitation includes a concept review for the week and covers a problem on velocity and acceleration of a point in a plane using polar coordinates.

Recitation 3: Motion in Moving Reference Frames

Engineering Dynamics

Prof. Vandiver goes over four classes of rotational problems: (1) rotation about fixed axis through center of mass; (2) fixed axis rotation not through center of mass; (3) unconstrained motion about center of mass; (4) rotation about moving points.

Lecture 12: Problem Solving Methods for Rotating Rigid Bodies

Prof. Vandiver introduces Lagrange, going over generalized coordinate definitions, what it means to be complete, independent and holonomic, and some example problems.

Lecture 15: Introduction to Lagrange With Examples

Prof. Vandiver goes over the cart and pendulum problem (2 DOF equations of motion), the center of percussion problem, then finally static and dynamic imbalance definitions.

Lecture 14: More Complex Rotational Problems & Their Equations of Motion

In this class, Prof. Vandiver uses two different notation systems. Please watch this video to see how the different notation systems interrelate.

Notation Systems

Prof. Vandiver goes over the concept questions for the week, the kinematic approach to finding generalized forces, the example of a wheel on moving cart with an incline, and the mass sliding on rod example.

Lecture 16: Kinematic Approach to Finding Generalized Forces

Prof. Vandiver goes over a new formula for computing torque about moving points, the hockey puck problem via direct method and Lagrange, condensing many forces to 1 force and 1 moment at COM, pendulum with Lagrange,  Atwood's machine, and falling stick.

Lecture 17: Practice Finding EOM Using Lagrange Equations

Prof. Vandiver goes over various problems to review for the quiz, such as sticking and sliding in a circular track, a rotating T-bar with an imbalance, a pendulum in an elevator, and other pendulum problems.

Lecture 18: Quiz Review From Optional Problem Set 8

Prof. Vandiver goes over the definition of the moment of inertia matrix, principle axes and symmetry rules, example computation of Izz for a disk, and the parallel axis theorem.

Lecture 11: Mass Moment of Inertia of Rigid Bodies

Prof. Vandiver goes over analyzing the response of a 2-DOF system to harmonic excitation with transfer functions, using a dynamic absorber to mitigate problem vibration, and does a demonstration of a dynamic absorber using a strobe and a vibrating beam.

Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions

Prof. Vandiver goes over wave propagation on a long string, flow-induced vibration of long strings and beams, application of the wave equation to rods, organ pipes, shower stalls with demonstrations, and vibration of beams (dispersion in wave propagation).

Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc

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