Math 252
Practice questions for Test 3
1. A mass of 2 kg is attached to a spring whose spring constant is 3 N/m. The medium oers a damping force of
magnitude 5 times the instantaneous velocity.
(a) Determine the steady-state position of the mass if it is
Math 252: Name that DE!
Name the type of differential equation. Types include:
separable
linear 1st order
exact
homogeneous
Bernoulli
reducible with u f ( Ax + By + C )
=
When appropriate, also specify the first step or steps you would take to solve the D
Linear Combination of Sine and Cosine
Any linear combination of a cosine and a sine of equal periods is equal to a single sine with the
same period but with a phase shift and a dierent amplitude.
In other words, given any c1 and c2 , we can nd A and such
Math 252 Quiz #4
June 10, 2011
Instructor: Patricia Wrean
Name: _
Total: 25 points
1. Evaluate the following.
a) L cfw_t 3e7t
e 2 s
b) L
s 3
1
(4 points)
Math 252
Quiz #4
2. Evaluate.
cfw_
a) L t (1 e3t )
Page 2
(5 points)
2
b) L cfw_te 2t cos 4t
Ma
Math 252 Quiz #2
May 9, 2011
Instructor: Patricia Wrean
Name: _
Total: 25 points
1. Solve the following initial value problem, given that y (0) = 3 and y(0) = 32 .
(3 points)
y + 2 y 24 y =
0
Math 252
Quiz #2
2. Consider the following differential equatio
Math 252 Quiz #3
May 27, 2011
Instructor: Patricia Wrean
Name: _
Total: 25 points
1. A mass of 0.50 kg is attached to a spring of constant 8.0 N/m. Assume that there is
no damping. The mass is released 6.0 cm below equilibrium with an upward velocity
of 0
Math 252 Quiz #1
April 21, 2011
Instructor: Patricia Wrean
Name: _
Total: 25 points
1. Solve the following differential equation. Give an explicit solution (i.e., solve for m).
(5 points)
dm
= 4 m2
dt
Math 252
Quiz #1
Page 2
2. Solve the following initial
Constant Coecients and Cauchy-Euler Equations
Gilles Cazelais
Constant Coecients.
A homogeneous second-order constant coecient equation is of the form
ay (x) + by (x) + cy(x) = 0.
(1)
To solve the equation, plug y = emx into (1) and deduce the characteris
Method of Undetermined Coecients
Problem. Find a particular solution yp of the constant coecients linear equation
an y (n) + + a2 y + a1 y + a0 y = g(x).
We assume that
g(x) = [polynomial] [exponential] [sinusoid].
More precisely, we assume that
g(x) = p(