Solutions for EWSEI W 4
5.15 Determine the phase shift and amplitude error in the output of an accelerometer that
has a natural frequency of25 kHz and a damping ratio of 0.1, when it is measuring
vibrations at 1 kHz.
Solution 5.15
Since]; = 25,0cfw_10 Hz

I Summer 2016 1
Due on June 14, 2016
ENME361: Assignment No. 2
Problem 1: (20) Obtain the equation of motion of the system shown below inFi'gure l by
using Lagranges equations. Use the generalized coordinate x0). Assume small '
displacements.
' 2k ,
I A
l

Summer 2016
Due on June 21, 2016
ENME361: Assignment No. 3
Problem 1: a) (10) For a spring-mass-damper system, = 50 and = 5000 /. Determine i)
the damped natural frequency when = 2 (c c is the critical damping coefficient), and ii) the
damping coefficient

V. Agarwal
Solutions for ENME361 Assignment No. 1
Problem 1: (20) In Figure E1.5, a slider of mass M r is located on a bar whose angular
displacement in the plane is described by the coordinate . The motion of the slider from
the pivot point is measured b

Name:_
ENME 361
Summer 2016
Examination #1
(June 23, 2016; Duration: 75 minutes)
PLEASE PAY ATTENTION TO THE FOLLOWING:
1. Please be neat.
2. Five Problems, not equally weighted.
3. State all assumptions made and provide steps but any incorrect statements

ENME361
Homework #4
(Due Thursday, Oct 13 2016)
1. An underdamped single degree-of-freedom system is travelling with a velocity Vo when
its base impacts a stationary rigid wall, as shown in Fig. 1.
a. Show that the resulting displacement response of the m

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 2: Modeling of Vibratory Systems (Chapter 2)
Due Date: Tuesday 14th of Feb. at 9:30am
Name:_; Section:_
1. Consider the mechanical spring system shown in
Figure 2. Assume that the bars a

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 1: Preliminaries from Dynamics (Chapter 1)
Due Date: Tuesday 7th of Feb. at 9:30am
Name:_; Section:_
Problems to be solved: 1.5, 1.6, 1.10, 1.14, 1.16.
The text and figures of the HW pro

7
Nov. 10th 2016)
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 peak frequency (where the amplitude of the response is maximum).
(d)

ENME 361 Fall Spring 2016: Vibrations, Controls, & Optimization I
ENME361
th
Homework #2
(Due Thursday, September 15 2016)
1. Consider the crank-mechanism system shown in
Figure 1. Determine the rotary inertia of this
system about the point O and express

ENME 361 - Fall 2016: Vibrations, Controls, & Optimization I
ENME361
Homework #3
th
(Due Tuesday, Sept 27 2016)
1. Determine the equation governing the system studied in Fig. 1 by carrying out a force/moment
balance.
x2
c
Jo, m2 o L1
kt
L2
k
m1
MEMs devic

ENME 361 - Fall 2016: Vibrations, Controls, & Optimization I
ENME 361
th
Homework #1
(Due Thursday, Sept 8 2016)
1.
Figure 1
Figure1
Also determine the kinetic energy of the system. (20 pts.)
2. Consider the pendulum of mass m attached to a moving pivot s

ENME361
Homework #5
th
(Due Thursday, October 20 2016)
1. For a uniform bar with a mass of m and a length of L. Considering small angular oscillations,
for what torsion stiffness is the system shown below unstable ?
g
O
2. Consider an electric motor driv

CHAPTER 5 Single Degree-of-Freedom Systems Subjected to Periodic Excitations
282
a) Expand Eq. (a) in a Fourier series and show that
1.5
1
tp 2p/v b
a0 0
f(t)/Fo
0.5
ai
0
1
T Mtp 2p/vo
tb Ntp
0
t
(a)
Amplitude
1
0.5
0
0.5
1
f(t)/F
x(t)/(F/k)
0
50
100
t

Exercises
5.20 The area of the hysteresis loop of a cyclically
2
loaded system, which is the energy dissipated per
forcing cycle, is measured to be 10 N # m, and the
measured maximum response Xo of the deection is
2 cm. Calculate the equivalent viscous da

ENME361: Vibrations, Controls, and Optimization I
Spring 2017
Feb 7, 2017
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 from

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 2: Modeling of Vibratory Systems (Chapter 2)
Due Date: Tuesday 14th of Feb. at 9:30am
Name:_; Section:_
1. Consider the mechanical spring system shown in
Figure 1. Assume that the bars a

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 8: Multi-Degree of Freedom System (MDOF) (Chapters 7 & 8)
Due Date: Tuesday, May 11nd, 2017, at 9:30am
Name:_; Section:_
Note: You are welcome to use MATLAB as needed, for all problems E

ENME361- Spring 2017
Vibrations, Control and Optimization I
Homework 6: SDOF Systems Subjected to Transient Excitations (Chapter 6)
Due Date: Thursday, April 20, 2017, at 9:30am
Name:_; Section:_
1. Consider a linear single DoF vibratory system governed b

ENME 361 Vibrations Quiz #5
' April 20, 2017; 15 minutes
The damped, single-DoF, linear oscillator shown in Figure 1 is subjected to a direct impulse force, F (I),
applied to the mass m. The force expression is given by:
1&1) hammer F(t) =fa 6(t). The res

Name: E E 1 I i 7
ENME 361 Vibrations Spring 2017 ' Quiz #6 (May 2nd, 2017; 10 minutes)
Consider the system shown in the gure below. Derive the equations of motion in the matrix
form for x and small 6 by using force balance and moment balance method. Base

syms k L_t
E=160*10^9;
L=100*10^-6;
b=2*10^-6;
b_t=2*10^-6;
h=2*10^-6;
k=(E*h*b^3*(4*L+L_t*(b/b_t)^3)/(L^3*(L+L_t*(b/b_t)^3);
ezplot(k,[10*10^-6,75*10^-6])
Published with MATLAB R2016b
1

ENME 361 - Spring 2016: Vibrations, Controls, & Optimization I
ENME361
Homework #2
th
(Due Thursday, Feb 16 2016)
2.27 Represent the vibratory system given in Figure
E2.27 as an equivalent vibratory system with mass m,
equivalent stiffness ke, and equival

Spring 2012
Name:
ENME361: SAMPLE MID-TERM EXAM I
PLEASE PAY ATTENTION TO THE FOLLOWING:
Be neat
Five Problems, not equally weighted
State all assumptions made and provide steps
Maximum time allowed for exam: 75 minutes
FWEV?
1. Problem 1: (20) A massless

Spring 2012
Name:_
ENME361: SAMPLE MID-TERM EXAM I
PLEASE PAY ATTENTION TO THE FOLLOWING:
1.
2.
3.
4.
Be neat
Five Problems, not equally weighted
State all assumptions made and provide steps
Maximum time allowed for exam: 75 minutes
1. Problem 1: (20) A m

ENME 350: HW1
Due September 8, 2014 by 8:00 AM in class
Fall, 2014
1. Please read Appendix A in the book on complex numbersit should be a review of what you
learned in high school math. Then do the following problems.
For the problems below, assume Z1=7+j

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 1: Preliminaries from Dynamics (Chapter 1)
Due Date: Tuesday 7th of Feb. at 9:30am
Name:_; Section:_
Problems to be solved: 1.5, 1.6, 1.10, 1.14, 1.16.
The text and figures of the HW pro