# 12-757   Vibrations

**Source**: https://cee.engineering.cmu.edu/education/course-descriptions/12-757.html
**Parent**: https://cee.engineering.cmu.edu/education/graduate/courses.html

This course is concerned with the response of discrete and continuous linear elastic systems subjected to dynamic excitation.

Newtons equations, Lagranges equations, and variational principles are used to formulate the problems; their solution is based primarily on direct methods, transform methods, and the modal method of analysis.

Applications to discrete systems, as well as various continuous systems involving individual components such as rods, beams, membranes and plates, are presented.

Numerical methods of solution are discussed, although emphasis is on problem solving and physical interpretation of results using analytical methods.\
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**Prerequisite(s):**Graduate standing or consent of the instructor