This course reviews momentum and energy principles, and then covers the following …
This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional …
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.013J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject merged with 2.003.
These dynamics course notes were authored by Dr. Elizabeth Croft (currently at …
These dynamics course notes were authored by Dr. Elizabeth Croft (currently at Monash University (elizabeth.croft@monash.edu) in 2004, and converted for open licensing (including figure creation) in 2019 by Dr. Agnes d'Entremont (adentremont@mech.ubc.ca) from the Department of Mechanical Engineering at the University of British Columbia, Vancouver, Canada (https://mech.ubc.ca).
The notes (are designed to be used for a second-year dynamics course in Mechanical Engineering, and cover planar rigid-body dynamics and an introduction to one degree-of-freedom vibrations. The order of topics has vibrations earlier in the series than typical, due to their use in an integrated course. This order matches the course timing of related ordinary differential equation solutions in the integrated mathematics and electric circuits courses.
These notes are intended to be skeleton notes, with substantial portions (diagrams, derivations, solutions) written in by students along with their instructor. Completed notes are included. PDF notes plus original LaTeX code and editable images (Powerpoint) are available at the link.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
This web page features a collection of Easy Java Simulations developed by …
This web page features a collection of Easy Java Simulations developed by secondary teachers for use in introductory high school physics courses. Topics include astronomy, momentum and collision, projectile motion, Gauss's Law and electric field, special relativity, and more. Each simulation is accompanied by a standards-based lesson plan and printable student guides. Users may run the simulations as a Java applet or may directly download a jar file version. The materials in this collection were created with Easy Java Simulations (EJS), a modeling tool that allows users without formal programming experience to generate computer models and simulations. To modify or customize the model, See Related Materials for detailed instructions on installing and running the EJS Modeling and Authoring Tool. This resource is part of Project ITOP (Improving the Teaching of Physics), a graduate program offered at University of Massachusetts-Boston. The archived computer models are hosted and maintained as part of the BU Physics Simulation collection.
The Early Universe provides an introduction to modern cosmology. The first part …
The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the classical cosmology, and later part with modern particle physics and its recent impact on cosmology. In the News For more about Professor Guth's work, listen to this interview from WBUR, Boston's National Public Radio news station. You may also be interested in this MIT Alumni Association Podcast Inflationary Cosmology—Is Our Universe Part of a Multiverse? with Professor Guth.
In this activity, students play the roles of "time travel agents" creating …
In this activity, students play the roles of "time travel agents" creating an advertisement for a geologic time period which has been assigned to them. They will use the Earth Science Reference Tables (available on the internet) to learn some basic facts about their assigned period. A rubric for assessing student understanding is provided.
Formative assessment questions using a classroom response system ("clickers") can be used …
Formative assessment questions using a classroom response system ("clickers") can be used to reveal students' spatial understanding. Students are shown this diagram and instructed to "Click within the layer that is entirely liquid."
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This activity is based around Macintosh software that I wrote to display …
This activity is based around Macintosh software that I wrote to display near real-time seismograms in classrooms with projection systems and internet communications. I use the display in courses at all levels, from large non-science courses to advanced graduate courses in seismology. In my introductory course, I have been fortunate to have a room with two projectors and large screens. That allows me to display the seismic monitor on one screen and use the other for that day's material. In smaller advanced courses I often project the real-time display on one screen while I use the chalk board during that part of the class that I use to cover new material. Although you might think that it's rare that an earthquake would occur during any given class, that's not true (have the students estimates the odds using the Gutenberg Richter relation if you doubt it). If needed, you can load specific earthquake signals (say from the night before) to talk about it at the beginning of a class period. Activity that occurs during class often leads to interesting discussions of earthquakes and tectonics. This activity uses online and/or real-time data, has minimal/no quantitative component, and can be used to address student misconceptions.
(Note: this resource was added to OER Commons as part of a batch upload of over 2,200 records. If you notice an issue with the quality of the metadata, please let us know by using the 'report' button and we will flag it for consideration.)
This lesson discusses the interior structure of the earth as defined by …
This lesson discusses the interior structure of the earth as defined by research on the behavior of seismic waves as they move through the layers inside of the planet. The lesson details both compositional layers as well as mechanical layers.
This video segment adapted from NASA's Goddard Space Flight Center shows how …
This video segment adapted from NASA's Goddard Space Flight Center shows how integral satellites are to everyday life and describes the different types, including orbital and geostationary.
In this demonstration, evidence of the Earth's rotation is observed. A tripod, …
In this demonstration, evidence of the Earth's rotation is observed. A tripod, swiveling desk chair, fishing line and pendulum bob (e.g., fishing weight or plumb bob) are required for the demonstration. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
This video segment adapted from NOVA tells the tragic story of two …
This video segment adapted from NOVA tells the tragic story of two Japanese seismologists who disagreed about the threat of earthquakes in the early twentieth century. Today, seismologists in California offer residents a probability of risk that an earthquake might occur.
This lesson on earthquakes is based on naturalist John Muir's experiences with …
This lesson on earthquakes is based on naturalist John Muir's experiences with two significant earthquakes, the 1872 earthquake on the east side of the Sierra Nevada Mountains, and the Great San Francisco Earthquake of 1906. Students will learn to explain that earthquakes are sudden motions along breaks in the crust called faults, and list the major geologic events including earthquakes, volcanic eruptions and mountain building, which are the result of crustal plate motions. A downloadable, printable version (PDF) of the lesson plan is available.
In this video segment adapted from NOVA, animations are used to show …
In this video segment adapted from NOVA, animations are used to show how the hills around Los Angeles were formed by earthquakes at small thrust faults that extend outward from the larger San Andreas fault.
In this video segment adapted from NOVA, a geologist digs a trench …
In this video segment adapted from NOVA, a geologist digs a trench along the San Andreas Fault to reveal three thousand years of earthquake history. Information from the layers of sediment may help geologists to predict earthquakes.
This video segment adapted from NOVA uses historical illustrations, photographs, and animations …
This video segment adapted from NOVA uses historical illustrations, photographs, and animations to explain how seismographs work, the difference between P and S waves, and the Richter scale.
This activity uses the free software 'Seismic Eruption' to visualize seismicity and …
This activity uses the free software 'Seismic Eruption' to visualize seismicity and volcanic activity in space and time and to explore the relationship of earthquakes and volcanic activiy to plate tectonics. Students run simulations on the Pacific coasts of South America and California and the mid-oceanic ridge in the Atlantic Ocean, answer questions, and construct a cross-section. A link to download the software is provided.
This interactive visualization adapted from NASA and the U.S. Geological Survey illustrates …
This interactive visualization adapted from NASA and the U.S. Geological Survey illustrates the concept of albedo, which is the measure of how much solar radiation is reflected from Earth's surface.
This module explores the composition of the earth's atmosphere, how temperature and …
This module explores the composition of the earth's atmosphere, how temperature and pressure vary in the atmosphere, and the scientific developments that led to an understanding of these basic concepts.
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