Credits: 3


Prerequisite: ENES220, ENES221, and MATH246; and (MATH206 or ENME202).
Restriction: Must be in Engineering: Mechanical program.
Fundamentals of vibration, controls and optimization. Analysis and design in time, Laplace and frequency domains. Mathematical description of system response, system stability, control and optimization. Optimal design of mechanical systems.

Semesters Offered

Fall 2017, Spring 2018, Summer 2018, Fall 2018, Winter 2019, Spring 2019, Summer 2019, Fall 2019, Spring 2020, Fall 2020, Winter 2021, Spring 2021, Summer 2021, Fall 2021, Spring 2022, Summer 2022, Fall 2022, Spring 2023, Summer 2023, Fall 2023, Fall 2024, Summer 2024, Spring 2024

Learning Objectives

In this course, the student will develop and/or refine the following areas of knowledge:

  • Model linear and nonlinear systems as combinations of springs, dampers, and masses. 
  • Analyze and interpret the response of mechanical systems to various types of excitations.
  • Predict qualitatively the response of systems based on the spectral content of the excitation and the frequency response characteristics of the system.
  • Minimize the effects of transient and harmonic excitations on systems and their support structures.


Topics Covered

Preliminaries from dynamics, modeling of vibratory systems, single degree-of-freedom systems: governing equations, free response, periodic excitations, and transient excitation. Multiple degree-of-freedom systems: natural frequencies, mode shapes, forced oscillations.

Learning Outcomes

  • an ability to apply knowledge of mathematics, science, and engineering
  • an ability to identify, formulate, and solve engineering problems

Additional Course Information


B. Balachandran and E. B. Magrab, Vibrations, Second Edition, CENGAGE Learning, Toronto, ON, 2009.

Class/Laboratory Schedule 

  • Two 75 minute lectures each week