2. CASE A. Mode 1 the amplitudes and frequencies of the response variables x1 and x 2
match that predicted by the analysis and they are 180 deg out of phase as expected. There
is a low frequency harmonic superposed on the response for x 2 which is probabl

Problem 1
&
m& + cx + kx = f a (t );
x
f a (t ) = pulse with magnitude 500kN and width 0.001s
CASE 1. A. c=400 N.s/m (underdamped)
CASE 1. B. c=4472.1 N.s/m (critically damped)
CASE 1.A. c=400 N.s/m (underdamped)
CASE 1. B. c=4472.1 N.s/m (critically damp

Solutions for Matlab/Simulink Project No. 1
A.
C = 0.1Cc
= 0.1
2
n
= 0.004
x ss = 0.001
Simulation
Analytical (see attached): x(t ) =
Fo
[1 exp( n t )cfw_cos d t
sin d t]
k
1 2
It can be seen that analytical and simulation match almost exactly.
B.
C = C

Some Tips for Studying for and Taking Timed Exams Professor J.C. Moosbrugger Department of Mechanical and Aeronautical Engineering Clarkson University Studying 1. Studying in small groups can be very effective. Do some of the following even if you're not

AE/ME 455 Formula Page for Exam II
Simple harmonic function
z (t ) = a cos t + b sin t = C cos(t ) = C sin(t + o )
b
a
= tan 1 ;
C = a2 + b2 ;
a
b
o = tan 1
Harmonically excited single degree of freedom system
2
2
& + 2n x + n x = n sin t
&
x
xss (t )

CLARKSON UNIVERSITY
Department of Mechanical and Aeronautical Engineering
Spring Semester 2005 AE/ME 455 Mechanical Vibrations
LEARNING OBJECTIVES FOR FINAL EXAM
These should serve as your "roadmap" in studying for the exam. They are a statement of what I

CLARKSON UNIVERSITY
Department of Mechanical and Aeronautical Engineering
Spring Semester 2005
AE/ME 455 Mechanical Vibrations
LEARNING OBJECTIVES FOR EXAM II
These should serve as your "roadmap" in studying for the exam. They are a statement of what I ex

CLARKSON UNIVERSITY
Department of Mechanical and Aeronautical Engineering
Spring Semester 2005 AE/ME 455 Mechanical Vibrations
LEARNING OBJECTIVES FOR EXAM 1
These should serve as your "roadmap" in studying for the exam. They are a statement of what I
exp