Episodes
This recitation introduces modal analysis and looks at a double pendulum problem.
Published 07/01/15
This recitation covers a Lagrange approach to a problem involving a cart and pendulum.
Published 07/01/15
This recitation covers a direct method of breaking down a problem involving a cart and pendulum.
Published 07/01/15
This recitation reviews free body diagram strategies, covers equations of motion for multiple degree-of-freedom systems, and addresses a dynamically balanced system.
Published 07/01/15
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.
Published 07/01/15
This recitation takes an in depth look at modal analysis for a double pendulum system.
Published 07/01/15
This recitation covers a steady state frequency response problem.
Published 07/01/15
This recitation covers generalized forces in a double pendulum. Questions are also addressed for an upcoming quiz.
Published 07/01/15
Published 07/01/15
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.
Published 07/01/15
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.
Published 07/01/15
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.
Published 07/01/15
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).
Published 07/01/15
Prof. Vandiver goes over the modal expansion theorem, computing mass and stiffness matrices, obtaining uncoupled equations of motion, modal initial conditions, damping in modal analysis, Rayleigh damping, and experimental fitting of damping ratios.
Published 07/01/15
Prof. Vandiver begins with an overview then goes over the linearization of a 2-DOF system, free vibration of linear multi-DOF systems, finding natural frequencies and mode shapes of multi-DOF systems, and mode superposition analysis of a 2-DOF system.
Published 07/01/15
Prof. Vandiver goes over the use of Rayleigh damping to model modal damping ratios, steady state response to harmonic excitation by the method of modal analysis, the direct method for assembling the stiffness of an N DOF system.
Published 07/01/15
This recitation includes a concept review for the week and covers an amusement park ride problem with velocity in translating and rotating frames. The class also covers questions regarding planar motion problems.
Published 07/01/15
Prof. Gossard goes over obtaining the equations of motion of a 2 DOF system, finding natural frequencies by the characteristic equation, finding mode shapes; he then demonstrates via Matlab simulation and a real 2 DOF system response to initial conditions.
Published 07/01/15
Prof. Vandiver goes over the damped response of spring-mass-dashpot system to ICs, the ballistic pendulum example, experimental determination of damping ratio, steady state linear system response to harmonic input, and a beam with a rotating mass shaker.
Published 07/01/15
Prof. Vandiver shows a vibration isolation system with a strobe light and vibrating beam, Hx/F transfer function using complex numbers, vibration isolation system design, predicting natural frequency by SQRT(g/delta), & vibration isolation of the source.
Published 07/01/15
Prof. Vandiver introduces the single degree of freedom (SDOF) system, finding the EOM with respect to the static equilibrium position, SDOF system response to initial conditions, phase angle in free decay, natural frequencies, and damping ratios.
Published 07/01/15
Prof. Vandiver starts with a review of applicable physical laws; he then goes over an example Class 4 problem with moving points of constraint, the tipping box problem, an alternative form of Euler's equation, and ends with a question and answer period.
Published 07/01/15
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.
Published 07/01/15
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.
Published 07/01/15
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.
Published 07/01/15