1. History of Dynamics; Motion in Moving Reference Frames 2. Newton's Laws & Describing the Kinematics of Particles 3. Motion of Center of Mass; Acceleration in Rotating Ref. Frames 4. Movement of a Particle in Circular Motion w/ Polar Coordinates R2. Velocity and Acceleration in Translating and Rotating Frames 5. Impulse, Torque, & Angular Momentum for a System of Particles 6. Torque & the Time Rate of Change of Angular Momentum R3. Motion in Moving Reference Frames 7. Degrees of Freedom, Free Body Diagrams, & Fictitious Forces 8. Fictitious Forces & Rotating Mass R4. Free Body Diagrams 9. Rotating Imbalance 10. Equations of Motion, Torque, Angular Momentum of Rigid Bodies R5. Equations of Motion 11. Mass Moment of Inertia of Rigid Bodies 12. Problem Solving Methods for Rotating Rigid Bodies R6. Angular Momentum and Torque 13. Four Classes of Problems With Rotational Motion 14. More Complex Rotational Problems & Their Equations of Motion R7. Cart and Pendulum, Direct Method Notation Systems 15. Introduction to Lagrange With Examples R8. Cart and Pendulum, Lagrange Method 16. Kinematic Approach to Finding Generalized Forces 17. Practice Finding EOM Using Lagrange Equations R9. Generalized Forces 18. Quiz Review From Optional Problem Set 8 19. Introduction to Mechanical Vibration 20. Linear System Modeling a Single Degree of Freedom Oscillator 21. Vibration Isolation 22. Finding Natural Frequencies & Mode Shapes of a 2 DOF System R10. Steady State Dynamics 23. Vibration by Mode Superposition 24. Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix R11. Double Pendulum System 25. Modal Analysis: Response to IC's and to Harmonic Forces 26. Response of 2-DOF Systems by the Use of Transfer Functions 27. Vibration of Continuous Structures: Strings, Beams, Rods, etc. R12. Modal Analysis of a Double Pendulum System