Fall 2017 - STMath 307 - Intro DE - Final Exam Formulas
g = 9.8 m/s2 = 32 f t/s2 ,
w = mg,
u dv = uv
v du
y(t) = Aer1 t + Ber2 t
y(t) = et (A sin(t) + B cos(t)
y(t) = Aer1 t + Bter1 t
y(x) = Axr
Math 307H, Spring 2012
Final Exam: Solutions
Page 1 of 7
1. (8 points) A mass of 100 kg stretches a (very big) spring by 2 m. Suppose that the mass is in a medium
that exerts a viscous resistance of 1
Math 307 I - Spring 2011
Practice Final
June 03, 2011
Name:
Student number:
1
2
3
4
5
6
7
8
9
10
Total
10
10
10
10
10
10
10
10
10
1
91
Complete all questions.
You may use a scientic calculator durin
Lecture 14. Damped Mechanical Vibrations. July 29, 2013
14.1. Deduction of the Basic Equation
Assume we have a spring with constant k. On this spring, there is a mass m. There is a damping
(resistance
Lecture 17. Laplace Transforms I. August 9, 2013
17.1. Denition
For a function y : [0, ) R, let
est y(t)dt, s 0,
(Ly)(s) :=
0
be another function Ly : [0, ) R. This new function Ly is called the Lapla
Lecture 16. Electrical Circuits. August 7, 2013
16.1. Physics
An electrical circuit consists of impressed voltage (=battery) giving voltage E(t), a resistor, a capacitor and an inductor.
An electrical
Lecture 15. Forced Mechanical Vibrations. August 5, 2013
15.1. No Damping
The same setting as in the last lecture. Assume we have an external force F (t). Then by Newtons
Second Law we have: mu = ku +
Lecture 18. Laplace Transforms II. August 12, 2013
18.1. Laplace Transform of Trig Functions
Let y(t) = cos(bt). Let us nd (Ly)(s). We have:
(Ly )(s) = s2 (Ly)(s) sy(0) y (0).
But y (t) = b2 cos(bt) =
Math 307K, Winter 2012
Practice Final Exam: Solutions
Page 1 of 7
1. (10 points) Solve the initial value problem
y + 2y + y =
1
e
et
0t 1
,
t >1
y(0) = y (0) = 0.
Before we apply the Laplace transform
Math 307 E - Summer 2011
Practice Midterm 2
August 17, 2011
Name:
Student number:
1
2
3
4
5
6
Total
10
10
10
10
10
3*
50
Complete all questions.
You may use a scientic calculator during this examina
SAMPLE FINAL EXAM, MATH 307, SPRING TERM
2017
INSTRUCTOR: PROFESSOR AKHTARI
First Name:
Last Name:
Time: 120 min.
Notes:
- This booklet contains 6 Problems.
- Some Problems have more than one part. Ma
Midterm 2 Practice Questions
1. Were given the equation
y + 2
5
t
y +
8
4
2
t
t
y=0
Knowing that one solution to this equation is y1 (t) = t2 , nd another solution.
1
2. Write down the trial solutions
Math 307 C - Spring 2011
Mid-Term Exam 1
April 20, 2011
Name:
Student number:
1
2
3
4
5
Total
10
10
12
8
10
50
Complete all questions.
You may use a calculator during this examination. Other electro
Math 307B Midterm 1
April 24, 2013
name
Honor Statement
I arm that my work upholds the highest standards of honesty and integrity, and that I have neither
given nor received any unauthorized assistanc
Spring 2012 Final Exam, Section F, page 1 of 6
1. (5 points) Solve the initial value problem
y + 2y = te2t ,
y(1) = 0.
Spring 2012 Final Exam, Section F, page 2 of 6
2. (5 points) Let y(t) be a soluti
Math 307F Final
March 21, 2013
name
Honor Statement
I afrm that my work upholds the highest standards of honesty and integrity, and that I have
neither given nor received any unauthorized assistance o
Math 307 E - Summer 2011
Practice Midterm 2
August 17, 2011
Name:
Student number:
1
2
3
4
5
6
Total
10
10
10
10
10
3*
50
Complete all questions.
You may use a scientic calculator during this examina
Information youll have for the nal:
Table of Laplace Transforms
f
L[ f ]
f
L[ f ]
1
1
s
1
s a
n!
s n +1
n!
( s a ) n +1
cos bt
s
s2 + b2
b
s2 + b2
(s a)
( s a )2 + b2
b
( s a )2 + b2
e at
tn
tn e at
s
Math 307K, Winter 2012
Practice Final Exam
Your Name
University of Washington
Student ID #
This exam is closed books. No aids are allowed for this exam. You can use any information on the
note sheet
Lecture 13. Mechanical Vibrations. July 26, 2013
13.1. Basic Models
Assume we have a spring-mass system. The mass m moves horizontally in one directions. Let u be
the elongation of the spring; u = 0 c
Lecture 19. Discontinuous Right-Hand Side. August 14, 2013
19.1. Multiplication by Exponent
Let y(t) = e2t cos(3t). Let us nd (Ly)(s). We have:
e
st 2t
e
e(s+2)t cos(3t)dt.
cos(3t)dt =
0
0
But we know
Lecture 5. Autonomous Equations. July 3, 2013
5.1. Denition
An autonomous equation is the equation y = f (y ), where the right-hand side does not depend on t.
For example, y = y 2 is an autonomous equ
Lecture 6. Eulers Method. July 5, 2013
6.1. Example 1
Consider the equation y = t + y 2 . We cannot directly solve it using the method of separation of
variables. Also, it is not linear, so we cannot
MATH 307D
Midterm 1
July 12, 2013
Student ID #
Name
Your exam should consist of this cover sheet, followed by 5 problems. Check that you have
a complete exam.
Unless otherwise indicated, show all yo
MATH 307D
Midterm 1
July 12, 2013
Student ID #
Name
Your exam should consist of this cover sheet, followed by 5 problems. Check that you have
a complete exam.
Unless otherwise indicated, show all yo
MATH 307D
Midterm 2 Solution
August 2, 2013
Student ID #
Name
Your exam should consist of this cover sheet, followed by 5 problems. Check that you have
a complete exam.
Unless otherwise indicated, s
MATH 307D
Midterm 2
August 2, 2013
Student ID #
Name
Your exam should consist of this cover sheet, followed by 5 problems. Check that you have
a complete exam.
Unless otherwise indicated, show all y
Math 307 E - Summer 2011
Pactice Mid-Term Exam
June 18, 2011
Name:
Student number:
1
2
3
4
5
6
Total
10
10
10
10
10
10
60
Complete all questions.
You may use a scientic calculator during this examin