Homework 3 Solution
MAE 3360
Due Sept. 20, 2016
Name_
The equations for an inverted pendulum are shown below. The force Fi is used to move the cart
in order to keep the pendulum mass vertical. The pendulum angle is continuously measured
and used to genera
c., 1.
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cur. fI e 11
can
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cfw_)/"de r :
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Formula Sheet
Integrating factors
for linear equations: IF = e
R
p(x)dx
R
My Nx
dx
N
R
Nx My
dy
M
for exact equations: (x) = e
OR (y) = e
Substitutions
y
x
OR v =
x
y
Bernoulli functions: u = y 1n
reduction to separation of variables: u = Ax + By + C wher
Formula Sheet
Basic Laplace Transforms
Lcfw_1 =
1
s
Lcfw_tn =
k
+ k2
s
Lcfw_cos kt = 2
s + k2
k
Lcfw_sinh kt = 2
s k2
s
Lcfw_cosh kt = 2
s k2
Lcfw_sin kt =
n!
, n = 1, 2, 3, . . .
sn+1
1
Lcfw_eat =
sa
Lcfw_(t a) = eas
s2
Lcfw_U(t a) =
eas
s
Additional L
l' i
m EXGI'CISBS AnSwors to selected oddnumbered problems begin on page ANS-27. ;
1" Problems 163 show mm the giVen functions are orthogonal
on the indicated interval.
1_ fri-l =.l.f;(I) = x2; [~12]
L frm =x.f2(x) = x3 + l; [ l, l]
1 fl(.r) = (ng) = .t'e
HW # 8 Due Tu 4/21 (marked with *)
ﬂ.”
ENGR 3300 TEST III study Guide
Useful formulas:
[CF-air [Cf(x,y)ds l:f(x(t),y(t)x/lx'(t)]2+Ly'(t)]2dt [ngdy
ﬁ<§€§w ﬂds llllr.?r.ndA
*1.Find a parametric equation for the following path
7"52. Determine whether the v
EE3300 TEST I Studyguide
A: Test Material for 2/24 (Tu)
1. a. Use a geometric series to find the fraction that is equivalent to the following repeating
decimal: Show your work.
0.581111
b. Suppose you go to work at a company that pays $0.02 for the first
Homework 1 Solution
MAE3360
Due Sept. 6, 2016
Name _
As shown below, two water tanks with the same diameter are connected by a long pipe. Initially, before
the water is allowed to flow through the pipe, the height H 1 of the water in tank #1 is greater th
Homework 2 Solution
MAE 3360
Due Sept. 13, 2016
Name_
1. Show the 4-quadrant position and then find the magnitude and angle of each of the
following complex numbers:
4
angle=ta n1
=0.9273
M = 32 +4 2=5
(a) 3+j4
3
(b) -3+j4
M = 32 +4 2=5
(c) -3-j4
M = 32 +
Exam #1 Solution
MAE 3360
Sept. 22, 2016
Name_
1. A spring-massdamper system is shown below; the displacement of the mass is x.
x
spring
damper
mass
input
force
Fi
Assuming the mass slides on a frictionless surface, the equations that define the dynamics
Quiz 12
MAE 3360
Oct. 18, 2016
Last Name, first_
A spring-mass damper system is shown below; the displacement of the mass is z.
z
spring
damper
mass
The differential equation for the position of the mass is as follows
0
0
z + 0.1 z +0.01 z=0 z
(a) Define
Homework 4 Solution
MAE 3360
Due Oct. 11, 2016
Name_
The Laplace transform of an engineering system is found to be the following:
100 (4 s 2+12 s +16)
Y ( s )=
( s+ 5 ) [ ( s+ 2 )2+3 2 ] [ ( s+15 )2+8 2 ]
(a) (50%) Obtain an equation for y(t) by finding t
Homework 5 Solution
Key Assignment
MAE 3360
Due Oct. 18, 2016
Name_
This problem pertains to improving the performance of a pile driver by changing the frequency of hitting
the top of the pile (steel beam) with force F i. The output of interest is the con
Problems are from 8th edition of text
Problem number :- 8-12 , 8-29, 8-44, 8-53, 8-62, 8-79, 8-117
Problem Statement:812 The electric power needs of a community are to be met by windmills with 40m diameter rotors. The
windmills are to be located where the
Assignment # 2 due on 9th October (Friday)
Chapter # 9
th
Problems are from 8 edition of text
Problem number: - 9-31, 9-32, 9-48, 9-86
931 An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90 kPa and
o
40 C, and is repeated 2500 times p
Assignment # 3 due on Monday (10/19/2015)
Chapter # 10
Problems are from 8th edition of text
Problem number: - 10-14, 10-22, 10-35
1014 A simple ideal Rankine cycle which uses water as the working fluid operates
its condenser at 40oC and its boiler at 300
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