Name ___________________________ Section _____________________
EM406
Examination I
September 23, 2004
Problem Score
1 /20
2 /25
3 /30
4 /25
Total /100
Show all work for credit
AND
Turn in your signed help sheet
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
EM406 Examination I: Problems and Solutions for Mechanical Systems, Exams of Engineering
The problems and solutions for examination i of the em406 course, focusing on mechanical systems. It includes problems related to springs, second order systems, slender beams, and packed objects. Students are required to calculate natural frequencies, identify damping types, determine equations of motion, and find steady state responses.
Typology: Exams
Pre 2010
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download EM406 Examination I: Problems and Solutions for Mechanical Systems and more Exams Engineering in PDF only on Docsity!
Name ___________________________ Section _____________________
EM
Examination I
September 23, 2004
Problem Score
Total /
Show all work for credit
AND
Turn in your signed help sheet
EM406 Examination I Problem 1 September 21, 2004
For all parts of problem 1 you must show all work for credit
Problem 1a A spring has a mass of 0.3 kg and a spring constant of 40 N/m. Estimate the natural frequency of the spring.
a) 0.0866 rad/s b) 11.55 rad/s c) 20 rad/s d) 24.08 rad/s
Problem 1b A second order system is excited harmonically, f(t) = 2 sin(0.785t) and the input and total response (transient and steady state) are shown below. What is the phase angle in radians between the input and the output?
k, m
0
1
2
3
4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tim e (s)
EM406 Examination I Problem 2 September 21, 2005
The slender beam of mass, M, and length, L, carries two masses and is supported by a spring k and a dashpot c. Using the angle, θ, measured from the static equilibrium point as a coordinate determine: a) the equation of motion in terms of θ b) the natural frequency in terms of the parameters given c) the critical damping in terms of the parameters given
k
m 3m
O
a
b
c M
L
EM406 Examination I Problem 3 September 21, 2004
A 4 kg piston slides with viscous friction inside a cylinder. The upper end of an elastic spring that supports the piston moves with a harmonic motion x 1 = 10 sin12t where x is in millimeters. The spring constant is 400 N/m and the damping constant is 20 N-s/m. Determine: a) the equation of motion for the mass b) the steady state response of the mass. c) A coworker was asked to find the range of frequencies where the amplitude is less than 11 mm and using Maple she found
Using her results, for what frequencies will the amplitude be less than 11 mm? x 1 = 10 sin12t
k
c
{ r =-0.3248666148 }, { r =-1.282365659 }, { r =1.282365659 },{ r =0.3248666148}