MECH 364
Assignment 2
Problems from the book: 2.2, 2.4, 2.6, 2.7, 2.8, 2.13, 2.16, 2.17, 2.22, 2.24
2.2
Consider the undamped, simple oscillator given by
2 x 0
x
n
It is known that x A sin n t repres
THE UNIVERSITY OF BRITISH COLUMBIA
DEPARTMENT OF MECHANICAL ENGINEERING
MECH 364 MECHANICAL VIBRATIONS
Mid-Term Examination
06 November 2008
Duration: 75 minutes
Open Book/Notes
Calculators or any oth
MECHANICAL VIBRATIONS
Solutions to the Final Examination 2
Problem 1.
(a)
Natural vibrations are oscillatory responses. Hence, both displacement and velocity
of the mass elements of the system will un
MECHANICAL VIBRATIONS
Solutions to the Mid-Term Examination 2
Problem 1
i)
Figure 1.
Shapes of the test responses
(a) Hammer test, (b) Shaker test.
-1-
Note that the response from the Hammer test is o
MECH 364 Mechanical Vibrations
SOLUTION GUIDELINES TO MID -TERM EXAMINATION
November 06, 2008
Problem 1
(a) Since the springs are uniform and one end of them is assumed fixed, the distributed
spring m
DEPARTMENT OF MECHANICAL ENGINEERING
THE UNIVERSITY OF BRITISH COLUMBIA
MECHANICAL VIBRATIONS
Sample Final Examination 2
Important Notes:
Duration: 3 hours
Open Book/Notes
No calculators
Fully answer
Mechanical Vibrations
Solution to Final Examination 1
Problem 1:
a) (i) Modal analysis decouples a coupled, complex, dynamic system. The uncoupled
equations are easier to analyze, and standard procedu
DEPARTMENT OF MECHANICAL ENGINEERING
THE UNIVERSITY OF BRITISH COLUMBIA
MECHANICAL VIBRATIONS
Mid -Term Examination 1
Duration : 50 minutes
Open Book / Notes
Fully answer both problems for full credit
MECH 364: MECHANICAL VIBRATIONS
Solution Guidelines for the Mid-Term Examination, March 2010
Problem 1
(a)
(i)
Undamped Natural Frequency ( n)
This is the frequency at which the system will oscillate
DEPARTMENT OF MECHANICAL ENGINEERING
THE UNIVERSITY OF BRITISH COLUMBIA
MECHANICAL VIBRATIONS
Sample Final Examination 1
Duration 3 hours
Open Book/Notes; A Non-programmable calculator is allowed
Full
Appendix A: Transform Techniques
Many people use transforms without even knowing it. A transform is simply a number,
variable, or function in a different form. For example, since 102 100, you can use
DEPARTMENT OF MECHANICAL ENGINEERING
THE UNIVERSITY OF BRITISH COLUMBIA
MECHANICAL VIBRATIONS
Sample Final Examination 3
Duration 3 hours
Open Book/Notes
Fully answer all three problems for full credi
Appendix C
Review of Linear Algebra
Linear algebra, the algebra of sets, vectors, and matrices, is useful in the study of
mechanical vibration and control systems in general and the state-space approa
MECH 364 Engine Vibration Due to Unbalanced Excitations (Experiment 1)
MECH 364, Experiment 1
Engine Vibration Due to Unbalanced Excitations
OBJECTIVES
1. To observe the effect of excitation frequency
THE UNIVERSITY OF BRITISH COLUMBIA
DEPARTMENT OF MECHANICAL ENGINEERING
MECHANICAL VIBRATIONS
Mid-Term Examination 3
Duration: 50 minutes
Open Book/Notes
Fully answer both problems for full credit
Cle
Mechanical Vibrations
SOLUTIONS TO MID -TERM EXAMINATION 3
Problem 1
(a)
Assume a suitable velocity profile (typically linear) and, through
integration, determine the kinetic energy of the distributed
MECHANICAL VIBRATIONS
SOLUTIONS TO FINAL EXAM 3
Problem 1
(a)
(i)
Piezoelectric Accelerometer:
Produces an electric charge that is proportional to the inertia force in the
mass element of the accelero
MECH 364 Mechanical Vibrations
SOLUTION GUIDELINES TO FINAL EXAMINATION
December 12, 2008
Problem 1
(i)
1. Specify the required level of isolation Ispec as a percentage. To allow for damping,
1.1I spe
THE UNIVERSITY OF BRITISH COLUMBIA
DEPARTMENT OF MECHANICAL ENGINEERING
MECH 364 MECHANICAL VIBRATIONS
Final Examination
12 December 2008
Duration: 150 minutes
Open Book/Notes
Calculators or any other
Note: Assignment 2 had given more problems than what was intended. For those students
who are highly motivated, we present below the solutions for the extra problems.
Solution 2.3
The knowledge of the
THE UNIVERSITY OF BRITISH COLUMBIA
DEPARTMENT OF MECHANICAL ENGINEERING
MECH 364 MECHANICAL VIBRATIONS
Mid-Term Examination
25 March 2010
Duration: 60 minutes
Open Book/Notes
A non-programmable cal
Mech 364 - Assignment #1
1.1 Explain why mechanical vibration is an important area of study for engineers.
Mechanical vibrations are known to have harmful effects as well as useful ones.
Briefly descr
Solutions to Practice Questions from Module 6: 1. a) If an object falls from a resting height of 490 m, how long does it remain in the air? Known: vi = 0 m/s a = g = -9.81 m/s2 y = -490 m Unknown: t=?
MECH 364 Assignment 5
Problems from the book: 6.16, 6.17, 6.19, 6.20, 6.21, 6.32
Solution 6.16
(a)
(i)
E = Youngs modulus of the beam material
I = 2nd moment of area of the beam cross-section, about i
Solution 5.4
Natural Frequencies and Mode Shapes
In a dynamic system there are some unique frequencies of motion at which the
displacements of its degrees of freedom will bear a constant proportion. T
Assignment #3: (Problems from the book) 3.1; 3.2; 3.3; 3.4; 3.6; 3.7; 3.8; 3.19; 3.26
Solution 3.1
(a)
Frequency Spectrum
This is a representation of the various frequency components of a signal, with
MECH 364 Mechanical Vibrations
SOLUTION GUIDELINES TO FINAL EXAMINATION
April 2010
Problem 1
(i)
Yes, I agree with this claim. It has been proved, at least for a single-degree-of-freedom
system and fo
4
distinct solutions for z, given by r = 81/3 = 2 and = + 23 k for k cfw_1, 0, 1.
9
(The restriction on the values of k comes from our assumption that is the principal
argument of z, which means that