ME450.3
Fall 2015
Homework#1
Due 9/11
Problem 1: A simple drawing and functional description of a hand-powered egg beater is shown. The goal is to
construct a mathematical model of this mechanical system by making free-body diagram for each element. The
i
ME 450.3
Computer Project #1
Fall 2015
due: October 9
Shown below is a schematic of a partial gear train used in common helicopter
gear drive boxes. J1 is the rotational inertia which the input torque Tm is applied.
Rotational stiffness is K1 and gears 1
ME 450
HOMEWORK SET 1
OUT: 09/02/15
Fall 2015
DUE: 09/11/15
Use a separate sheet to answer each problem. Also write your own name and problem number on
each sheet you hand in.
Problem 1: (20pts)
1) Describe in your own words, what do you consider as a sys
ME 450:2
Fall 2014
HOMEWORK ASSIGNEMNT #6
Due: Wednesday Oct. 15, 2014
1. In the mechanical system shown below all elements are assumed to be linear except the
frictional damper that exerts a nonlinear force FNLD on mass m2. The nonlinear damping
force is
ME 450.3 Homework# 2
Fall 2015
Due: September 25
In the mechanical system shown in Figure 1, both springs are fully relaxed when the lever is horizontal.
Furthermore, the equivalent viscous damping associated with the angular velocity of the lever is deno
ME 450.2
Fall 2014
HOMEWORK ASSIGNEMNT #1
Due: in class Wednesday September 10, 2014
Read http:/en.wikipedia.org/wiki/Moment_of_inertia before you start to work on
this homework.
Problem 1. In the mechanical system shown below all elements are assumed to
Solutions to Hw#3
Problem 1,
EoM:
mv mg Frope
J r F
(1)
(2)
rope
where
Frope k * k * ( x r )
Part I. I/O model
From (2), x
J
r
rk
And
x
J
r ,
rk
x
J ( 4)
r
rk
Plug them into eq. (1),
J ( 4)
r mg k ( x r )
m
rk
=>
mJ ( 4)
J
(mr ) mg
rk
r
Part II
ME 450:2
Fall 2014
HOMEWORK ASSIGNMENT #3
(Due: in class, Friday September 19, 2014)
Problem 1. A new ride at an amusement park involves jumping from a Ferris wheel with an
elastic rope (with a spring constant k) attached to the jumper as shown below. The
ME 450.2
Fall 2014
HOMEWORK ASSIGNEMNT #4
Due: in class Friday September 26, 2014
Problem 1. A first-order model of a dynamic system is
2 y 5 y 5u (t )
with initial condition y(0) = 2. Find and sketch the response of this system to the unit step
input u (
ME450.3
Fall 2015
Homework# 4
Due October 23
1. A 5 kg watermelon was initially cooled to 5 0 C , but is exposed to 30 0 C with free convection at
the picnic.
Derive the differential equation for watermelon temperature variation and solve it. Assume that
ME 450.1
Fall 2014
Homework 5
Due: In class, Wednesday October 8
1. [10 pts] The output voltage of a first-order electric circuit subjected to a step change in the input
voltage at t = 0 is shown in the figure below:
The system and the output response is
ME 450.1
Fall 2014
Homework 2
Due: In class, Friday 9/19
1. [12 pts] For the following systems, determine the degrees of freedom (DOFs) and the order of
the system.
(1) A multiple mass-spring-damper system with a driving force Fi
The DOF is _
The order of
ME 450.1
Fall 2014
Homework 4
Due: In class, Friday October 3
1. [20 pts] Examine the LTI mass-spring-damper system shown below:
F
(1) The IO model relating x to F is given by
&
&
a) m& + cx + (k1 + k 2 ) x = cF + k 2 F
x
&
&
b) cm& k 2 m& + k 2 cx + k1 k
FIGURE 8.1 9
Magnitude
asymptotes of
poles and zeros
used in the
example.
Chapter 8 Frequency Response Methods
from 0° to ~360°. Because 62 = 180° — 01 and = 180° — 0:, the phase
q.’>(co) = —2(61 + 6:). The magnitude and phase characte
ME 450.1
Fall 2014
Homework 7
Due: In class, Wednesday November 5
(50 pts) Consider the circuit system shown below:
(1) (10 pts) Let e13 be the output of interest, a state model for the circuit is
a)
R
1
1
&
i1 = 2 i1 e4 g + e s
L
L
L
R3
R + R2
1
&
e4 g =
ME 450.1
Fall 2014
Homework 1
Due: In class, Wednesday 9/10
1.
[10 pts]
(1) As another proof that energy stored in an element cant change instantaneously, consider a
spring of stiffness k with one end fixed and the other end free to move in x direction. P
ME450.3
Homework#5
Fall 2015
Due: November 20
Consider a single link robot manipulator driven by a DC motor. The mass and
length of the link are 30 kg. and 1.2 meter, respectively. The payload is 20 kg. Following
Luhs paper [1], design a position control
ME 450.3 Fall 2015
Homework# 3
Due 10/16
Consider the electrical network shown below.
1. Derive a state space model for the network with voltages eo and ei as output and
input, respectively.
2. Obtain the transfer function and input/output differential eq
ME45 0.3 Computer Proj ect#2 Fall 2015 Due: November 6
The system shown below uses a ﬁeld—controlled DC motor to drive a variable—
speed drilling apparatus. The armature circuit of the motor is driven by a power supply
° having a constant voltage source e
ME 450
OUT: 09/09/15
HOMEWORK SET 2
Fall 2015
DUE: 09/18/15
Use a separate sheet to answer each problem. Also write your own name and problem number on
each sheet you hand in.
Problem 1: (30pts)
A homogeneous disk (having an outer radius of R and of mass
ME450.3
Fall 2015
Homework# 6
Due 12/09
Consider the disk drive head position control system shown in Figure. Let
Y ( s)
G(s)
E ( s)
a. Obtain the open-loop transfer function G(s) .
b. Sketch the asymptotic Bode magnitude and phase plots for G( j ) and c
ME 450.1
Fall 2014
Homework 9
Due: In class, Friday Dec. 5
(50 pts) An electro-mechanical vibrator is schematically shown below. The electromagnetic force induced in the mass m is Fm = i and the induced voltage is e34 = v
1. (15 pts) The IO model relating
ME 450.1
Fall 2014
Homework 6
Due: In class, Monday October 13
1. [25 pts] A second-order system is described by the IO model below:
0.5 2.5 y 50 y 100u
y
(1) [2 pts] The natural frequency and damping ratio of the system are
a) n 5 ,
5
2
b) n 2 5 ,
5
4
JJ-(
t; - a)
J
f 0 ) clt -:fco)
q/ff6
()
dJ
J~
c-t-o) d t
lec+t-,~ra.1 SlJs.!em
-:; '
ct>
0
cfw_I'll):
J0 Ct)est ol
(1
-: : -
e -st ( t"!:'o -: : I
esb-'oY-
.
J
( avod.fr; r1nd uc+o r
* ~)~'r
- +
cLss; poJiVt:J e ,~
F"'t'R.J~ S<k> rri
F 'nnrYJtFYJma':)
c