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 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

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

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

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

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
th
Homework #5
(Due Thursday, March 27 2014)
1.
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 modu

ENME361
th
Homework #6
(Due Thursday, April 3 2014)
1.
A reciprocating pump, weighing 150 lb, is mounted at the middle of a steel plate of thickness
0.5 in., width 20 in., and length 100 in., clamped along two edges as shown in Fig. 1. During
operation of

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
Homework #3
th
(Due Thursday, Feb 27 2014)
1. Derive the governing equation of motion for the rocker-arm valve assembly shown in
Figure 1 using Lagranges Equation. Assume small motions

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
th
Homework #9
(Due Thursday, May 1 2014)
1.
Sandblasting is a process in which an abrasive material, entrained in a jet, is directed onto the
surface of a casting to clean its surface

May 13th 2014)
1.
10
A two-mass system consists of a piston of mass m1, connected by two elastic springs, that
moves inside a tube as shown in Fig. 1. A pendulum of length l and end mass m2 is connected
to the piston as shown in Fig. 1.
(a) Derive the equ

Review Problems
Exam # 2
ENME 361
Mechanical Vibration
Free Responses
Chapter 4
Introduction
Free Responses of Undamped & Damped Systems
Stability of a Single Degree-of-Freedom System
Machine Tool Chatter
Single Degree-of-Freedom Systems with
Nonlin

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
Date: 3/13/14
Time: 1:15hrs
Exam #1
Open Book & Notes
Please attempt the following questions
1. A cylinder of mass m and mass moment of inertia J0 is free to roll without slipping but

Preliminaries from Dynamics
(ENME 361)
Chapter 1
University of Maryland
B. Balachandran & E. Magrab
Contents
Preliminaries from Dynamics
Kinematics of Particles & Rigid Bodies
Generalized Coordinates & Degrees-of-Freedom
Dynamics of Particles & Rigid

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
Homework #3
th
(Due Thursday, Feb 27 2014)
1. Derive the governing equation of motion for the rocker-arm valve assembly shown in
Figure 1 using Lagranges Equation. Assume small motions

HOMEWORK #5 SOLUTIONS
1. Verify that:
Lcfw_cos at =
s
, s>0
s + a2
2
Solution:
Lcfw_cos at = G ( s ) = cos ate st dt
0
e
[ s cos at + a sin at ] |
0
s2 + a2
s
=2
, s>0
s + a2
=
st
2. Determine the Laplace transform of the following signal, expressed in t

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

th
8
April 17 2014)
1.
The peak amplitude of a single-degree-of-freedom system, under a harmonic excitation,
is observed to be 0.2 in. If the undamped natural frequency of the system is 5 Hz, and the
static deflection of the mass under the maximum force i

May 13th 2014)
1.
10
A two-mass system consists of a piston of mass m1, connected by two elastic springs, that
moves inside a tube as shown in Fig. 1. A pendulum of length l and end mass m2 is connected
to the piston as shown in Fig. 1.
(a) Derive the equ

ENME 361 - Spring 2014: Vibrations, Controls, & Optimization I
ENME361
th
Homework #9
(Due Thursday, May 5 2014)
1.
Sandblasting is a process in which an abrasive material, entrained in a jet, is directed onto the
surface of a casting to clean its surface

Fall 2015
Due at 9:30 A.M. in class on Thursday December 03, 2015
ENME361: Assignment No. 11 (Total Marks = 100)
1. Derive the equations of motion of the system shown in Figure below, which is an extended
version of a two degree-of-freedom system discusse

Solutions for ENME361 Assignment No. 4
1. Obtain the equation of motion for the system with rotating unbalance shown in Figure
below by using Lagranges equations.
Solution
The position vector from point O to mass mo is
(
) (
)
rm = h cos t i + x + sin t j

Fall 2015
Due at 9:30 A.M. in class on Thursday December 03, 2015
ENME361: Assignment No. 10 (Total Marks = 100)
1. Derive the equations of motion of the systems shown in the two figures below and present the
resulting equations in each case in matrix for

Solutions for ENME361 Assignment No. 5
1. 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 = 400 MPa. Each of these legs has a
length of 0.5 m and a

Fall 2015
Due at 9:30 A.M. in class on Thursday October 29, 2015
ENME361: Assignment No. 8 (Total Marks = 100)
1. A motor of mass m is mounted at the end of a cantilever beam and it is found that the beam
deflects 10 mm. When the motor is running at 1800