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 represents the complete solution to this
system equation.
(a)
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 other electronic devices are not allowed
Fully answer both
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 undergo cyclic variations in natural
vibration. That mean
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 oscillatory and decaying. This is the
behavior of an und
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 mass can be lumped at the other (free) end at one-third
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 all three problems for full credit
Define your notation
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 procedures and results are available.
(ii) The dynamic perform
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
This exam paper contains 4 pages including the cover s
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 in response to an initial condition
excitation in a giv
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
Fully answer all three problems for full credit
This exam p
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 the exponent (2) to represent the number 100. Doing thi
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 credit
Give all your assumptions and details of derivations
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 approach in
particular. In practical mechanical vibration sys
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 on vibration response, notably the large
response at a
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
Clearly state all the assumptions made and give all steps
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 distributedparameter system in terms of the velocity at the coordi
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 accelerometer. This charge measures the acceleration
of the mas
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 spec
increase this by 10%. Compute the corresponding trans
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 electronic devices are not allowed
Fully answer all pa
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 position x alone of a mass at a given time t and the f
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 calculator is allowed. No other electronic
devices are all
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 describe five practical examples of good vibrations and five
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=? Solution: 1 y = vi t + 2 at 2
1 -490m = (0)t + 2 (-9.8
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 its neutral
axis of bending (This may vary along the bea
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. These
frequencies are the natural frequencies of the sys
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, within a range
of frequencies. Typically, both the magnitud
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 for a two-degree-of-freedom system, that the force transm
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 < .) So the three solutions are 2 cis( 79 ),
2 cis( ) a