Spring 2011 Due on February 8, 2011 ENME361: Assignment No. 1 1.4 Show that the acceleration of the particle in the rotating frame of Example 1.3 is
& & a = ( &p 2 y p 2 x p y p )e1 + ( &p + 2 x p 2 y p + x p )e2 x y
where is the magnitude of the angular

February 09, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Homework#1:
Problem1.4
Show that the acceleration of the particle in the rotating frame of Example 1.3 is
a = p 2 y p 2 x p y p e1 + p 2 x p 2 y p x p e2
x
y
(
)
(
)
where is

Due Date: Feb 8, 2007
ENME 361 Homework 1
Q1: Consider the disc rolling along a line in Figure 1. The disc has a mass m and rotary inertia JG about
the center of mass G. (a) How many degrees of freedom does this system have? (b) Determine the
kinetic ener

7
th
April 10 2014)
1. For the SDOF system of Fig. 1, given m=10 kg, k = 4000 N/m, and c =200 Ns/m, calculate:
(a) The undamped natural frequency.
(b) The damped natural frequency.
(c) The resonance frequency.
(d) The peak frequency (where the amplitude o

ENME361: Vibrations, Controls and Optimization I
Winter 2012
January 6, 2012
Solutions for ENME361 HW 1
1.5 In Figure E1.5, a slider of mass Mr is located on a bar whose angular displacement in
the plane is described by the coordinate . The motion of the

February 08, 2011
ENME 361: Vibrations, controls and optimization I
Spring 2011
Homework#1:
Problem1.4
Show that the acceleration of the particle in the rotating frame of Example 1.3 is
a = p 2 y p 2 x p y p e1 + p 2 x p 2 y p x p e2
x
y
(
)
(
)
where is

March 11, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Homework#4
Problem4.2:
A load of mass m is suspended by an elastic cable from the mid-span of a beam, which is
held fixed at one end and is free at the other end, as shown in Fig

ENME361: Vibrations, Controls, and Optimization I
Winter 2015
January 8, 2015
Solutions for HW 1
1.5 In Figure E1.5, a slider of mass Mr is located on a bar whose angular displacement in the plane is
described by the coordinate . The motion of the slider

ENME 361 - Fall 2007
Name:_
SAMPLE MID-TERM EXAM II
PLEASE PAY ATTENTION TO THE FOLLOWING:
1.
2.
3.
4.
Be neat.
Four Problems, not equally weighted.
State all assumptions made and provide steps.
Maximum time allowed for exam: 75 minutes.
Problem 1: (40).

March 29, 2011
ENME 361: Vibrations, controls and optimization I
Spring 2011
Homework#5
Problem4.3
A 25 kg television set is placed on a light table supported by four cylindrical legs made
from a steel alloy material with a Youngs modulus of elasticity E

March 29, 2011
ENME 361: Vibrations, controls and optimization I
Spring 2011
Homework#5
Problem4.3
A 25 kg television set is placed on a light table supported by four cylindrical legs made
from a steel alloy material with a Youngs modulus of elasticity E

University of Maryland
A. James Clark
School of Engineering
Mechanical Engineering Department
Vibration, Controls and Optimization I
ENME 361, Spring 2010
Exam # 1
At the end of the exam, sign the honor pledge in the space below:
I pledge on my honor that

ENME361: Vibrations, Controls and Optimization I
Winter 2012
January 20, 2012
Solutions for ENME361 HW 3
5.22 Determine an expression for the output of an accelerometer with the damping factor
and natural frequency n, when it is mounted on a system execu

Due Date: Feburary 15, 2007
ENME 361 Homework 2
Q1: Consider the crank-mechanism system shown in Figure 1, and determine the rotary inertia for the
system about the point O, and express it as a function of the angular displacement . The disc has a
rotary

ENME361: Vibrations, Controls and Optimization I
Winter 2012
January 12, 2012
Solutions for ENME361 HW 2
3.30 Derive the governing equation for the single-degree-of-freedom system shown in
Figure E3.30 in terms of when is small, and obtain an expression f

February 22, 2011
ENME 361: Vibrations, controls and optimization I
Spring 2011
Homework#3:
Problem3.8
Determine the equation governing the sysetem studied in Example 3.15 by carrying out a
force balance.
Solution
The free body diagrams are show below.
Th

February 09, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Homework#2:
Problem2.6:
Consider the mechanical spring system shown in Figure E2.6. Assume that the bars are
rigid and determine the equivalent spring constant ke , which we c

February 04, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#2
Problem1:
1. Using Taylors Series Expansion, show that cos ( z ) = 1
12
z + for z 0 .
2
1
cos ( z ) 1 z 2
2
2. Calculate the relative error e =
cos ( z )
Solution
The

March 02, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Homework#3:
Problem3.3:
A vibratory system with a softening nonlinear spring is governed by the following
equation,
m + cx + k x x 3 = 0
x
(
)
Determine the static-equilibrium po

March 4, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#5
Problem1:
Each leg of the angle bracket shown has a uniformly distributed mass m and length L.
The angle 2 between the two legs is fixed.
a) Using Lagranges equation, and a

February 25, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#4
Problem1:
a) Using Laplace Transform table in the next page, derive an expression for X ( s ) , in
Laplace Domain, given the follwing homogeneous ordinary differential

University of Maryland
A. James Clark
School of Engineering
Mechanical Engineering Department
Vibration, Controls and Optimization I
ENME 361, Spring 2010
Exam # 2
At the end of the exam, sign the honor pledge in the space below:
I pledge on my honor that

Spring 20 1 7
Name:
Section:
ENME361: MID-TERM EXAM I
PLEASE PAY ATTENTION TO THE FOLLOWING:
Write down your Name and Section number on EACH page.
This is a closed book/notes exam. No calculator or formula sheets are allowed.
Please write neatly.
There ar

February 02, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#1
Given the planar vector r ( x, y, t ) as r = [ y l cos ] i + l sin , where l is a constant, i
j
j
and are the Cartesian unit vectors, y = y ( t ) and = ( t ) . If v = d

March 11, 2010
ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#6
Problem1:
For the vibratory system described by the equation
( t ) + 4 x ( t ) + 3x ( t ) = f ( t )
x
a) Derive an expression for the response x ( t ) to an impulse input

ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#10
A damped second order system is described by the 2nd order differential equation:
m( t ) + cx ( t ) + kx ( t ) = f ( t )
x
a) Determine the time response of the system displacement x (

ENME 361: Vibrations, controls and optimization I
Spring 2010
Quiz#7
A SDOF system is subjected to a rectangular impulse f ( t ) = f0 u ( t ) u ( t t 0 ) , where
t 0 = 1.0 s and f0 = 1.0 N. Assume that the system parameters are: k = 16 N/m, c = 0.8
N.s/m,

Name: B. Balachandran
ENME361
Fall 2010
Examination #2
(November 9, 2010; Duration: 9:30 AM to 10:45 AM)
PLEASE PAY ATTENTION TO THE FOLLOWING:
1. Be neat.
2. Five Problems, not equally weighted.
3. State all assumptions made and provide steps.
1. (30)
a)

Name: /M0Z I
. ENNIE 361 Vibrations Spring 2017 Quiz #1
1) (5 pts) Consider vector u and v, if
u-2'+1' k
"3 2"
v 3i+3' 3k
2 21 4
and u and v are orthogonal to each other. Find the a: that satises the condition \:
j37'_ O .6 (2" 3M3; 3+(llCZ)+(-e(\(.%
I+7F

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 3: Modeling of Vibratory Systems, Single DOF Systems (Chapter 2 and 3)
Due Date: Thursday 23rd of Feb. at 9:30am
Name:_; Section:_
1. Using the VCL, run Example 2.7 (Springs in Parallel)

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 7: Multi-Degree of Freedom System (MDOF) (Chapter 7)
Due Date: Tuesday, May 2nd, 2017, at 9:30am
Name:_; Section:_
a) Equation of Motion: Force Balance Method (natural frequency and mode