Free Vibration of SDOF Torsional
Systems with Viscous Damping
Free Vibration of Nonlinear Systems
Lecture 8:
Forced Vibration of SDOF Systems
Examples
Mechanical Vibrations
Lecture 7:
With many figures and models from Mechanical Vibrations, S. S. Rao
Fre

Forced Vibration of Damped SDOF
Systems
Lecture 10:
Response of a Damped System
Under the Harmonic Motion of the Base
Examples
Mechanical Vibrations
Lecture 9:
With many figures and models from Mechanical Vibrations, S. S. Rao
Forced vibration -1
From t

Faculty of Engineering and Applied Science
Mechanical Vibrations
MECE 3210U
Experiment # 2
Free Vibration of Single Degree of Freedom Systems
Revised by
Dr. A. Mohany, N. Arafa
Chris Janotta
100458698
Alvin Chan
100395484
Kevin Lam
100458260
Lap Fung Matt

Degree of Freedom
Spring and Stiffness
Mass or Inertia Elements
Damping
With many figures and models from Mechanical Vibrations, S. S. Rao
Mechanical Vibrations
Lecture 2:
Introduction -1
Degree of freedom
Two degree of freedom system
Three degree of

Degree of Freedom
Spring and Stiffness
Mass or Inertia Elements
Lecture 3:
Damping
Simple Harmonic Motion
Free Vibrations of SDOF
Mechanical Vibrations
Lecture 2:
With many figures and models from Mechanical Vibrations, S. S. Rao
Introduction -1
Dampi

Damping
Simple Harmonic Motion
Free Vibrations of SDOF
Lecture 4:
Free Vibration of undamped SDOF
Examples
Mechanical Vibrations
Lecture 3:
With many figures and models from Mechanical Vibrations, S. S. Rao
Free vibration -1
Free Vibration of SDOF Sys

Examples
Free Vibration of Undamped
SDOF Systems
Lecture 5:
Free Vibration of damped SDOF
Examples
Mechanical Vibrations
Lecture 4:
With many figures and models from Mechanical Vibrations, S. S. Rao
Free vibration -1
Free Vibration of SDOF Systems
vs. d

Free Vibration of damped SDOF
Log Decrement for Damping
Calculation
Lecture 6:
Free Vibration of Torsional System
Examples
Mechanical Vibrations
Lecture 5:
With many figures and models from Mechanical Vibrations, S. S. Rao
Free vibration -1
Free Vibrati

Example
Forced Vibration of SDOF Systems
Lecture 8:
Forced Vibration of SDOF Systems
Mechanical Vibrations
Lecture 7:
With many figures and models from Mechanical Vibrations, S. S. Rao
Forced vibration -1
Forced Vibrations
2nd order
linear
non-homogeneou

Mechanical Vibrations
Lecture 8:
Forced Vibration of Undamped
SDOF Systems
Lecture 9:
Forced Vibration of Damped SDOF
Systems
With many figures and models from Mechanical Vibrations, S. S. Rao
Forced vibration -1
Response of Forced Undamped System
st
1

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FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE 3210U Mechanical Vibrations
Assignment No. 1
Due Date: Thursday, Feb. 11th, 2016 (5:00 pm)
1. The static equilibrium position of a massless rigid bar, hinged at point O and connected
with springs k1 and k2 i

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. l of 6
Student Number:
Print Name:
University of Ontario Institute of Technology
Faculty of Engineering and Applied Science
MECE3210U Mechanical Vibrations
Dr. A. Mohany Makeup Mid-term Examination March 1, 2014
Time: 1 hour and 30 minutes. Clos

FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE 3210U Mechanical Vibrations
Assignment No. 1
Due Date: Monday, Jan. 27th, 2014 (5:00 pm)
1. Develop a mathematical model for the tractor and plow shown below by considering the
mass, elasticity, and damping

FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE3210U Mechanical Vibrations
Assignment No. 4
Due Date: Monday, March 24th, 2014 (5:00 pm)
1. Drive the mass matrix and the stiffness matrix and define the coupling type in the system
shown below.
k
X
3
M3
k
X

FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE 3210U Mechanical Vibrations
Assignment No. 2
Due Date: Friday, Feb. 14th, 2014 (5:00 pm)
1. A massless bar of length 1 m is pivoted at one end and subjected to a force F at the other
end. Two translational d

FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE 3210U Mechanical Vibrations
Assignment No. 3
Due Date: Friday, Feb. 28th, 2014 (5:00 pm)
1. A spring-mass system, resting on an inclined plane, is subjected to a harmonic force as
shown below. Find the respo

Sample Calculation Part A:
Weight
Calculated Spring Constant
Average Spring Constant:
Percentage of Error:
Spring Constant
Average Spring
Constant
M(kg)
0
0.4
0.8
1.2
1.6
2
Deflection x(mm)
Loadin
g
Unloading
0
0
10
9.2
19.6
19
29.6
29
39.6
39.4
49.2
49.2

ENGR 3210U Mechanical Vibrations
Midterm Exam Winter 2009
Date: Monday, March 9, 2009
Instructor: Prof. E. Esmailzadeh, PEng
Time: 90 minutes
SOLUTIONS
Name:
Student ID #:
Note:
This test contains 5 problems.
Answer all problems.
Useful formulas are liste

FACULTY OF ENGINEERING AND APPLIED SCIENCE
MECE 3210U Mechanical Vibrations
Assignment No. 2
Due Date: Thursday, Feb. 25th, 2016 (5:00 pm)
1. A spring-mass system, resting on an inclined plane, is subjected to a harmonic force as
shown below. Find the res