David Gamble Brewer MAT 275 ONLINE B Spring 2018
Assignment MAT 275 TEST 2 due 04/16/2018 at 02:52pm MST
Problem 1. 1. (1 point)
Find the solution to initial value problem
d2y
dt2−8dy
dt +16y=0,y(0) = 5,y0(0) = 7
y(t) = .
Answer(s) submitted:
•5eˆ(4t)-13eˆ(4t)t
(correct)
Problem 2. 2. (1 point) Find a particular solution to
y00 −2y0+y=14.5et.
yp=
Answer(s) submitted:
•eˆt+teˆt+(((29eˆt)(tˆ2))/4)
(correct)
Problem 3. 3. (1 point) For the differential equation
s00 +bs0+3s=0,
find all the values of bthat make the general solution over-
damped, those that make it underdamped, and those that make
it critically damped.
(For each, give an interval or intervals for b for which the
equation is as indicated. Thus if the the equation is overdamped
for all b in the range 2<b≤3and 4≤b<∞, enter (2,3],
[4,infinity); if it is overdamped only for b =8, enter [8,8].)
If the equation is overdamped, b∈
If the equation is underdamped, b∈
If the equation is critically damped, b∈
Answer(s) submitted:
•(-infinity,2sqrt(3)]U[2sqrt(3),infinity)
•[-2sqrt(3),2sqrt(3)]
•[2sqrt(3)]
(score 0.333333333333333)
Problem 4. 4. (1 point) Determine whether the following
pairs of functions are linearly independent or not on the whole
real line.
? 1. f(t) = tand g(t) = |t|
? 2. f(x) = e18xand g(x) = e18(x−1)
? 3. f(θ) = 18cos3θand g(θ) = 72cos3θ−54cosθ
Answer(s) submitted:
•Linearly dependent
•Linearly dependent
•Linearly dependent
(score 0.6700000166893005)
Problem 5. 5. (1 point)
Find the solution to the boundary value problem:
d2y
dt2−11 dy
dt +24y=0,y(0) = 7,y(1) = 8
y=
Answer(s) submitted:
•((7-(((7eˆ8)-8)/(eˆ8-eˆ3)))eˆ(8t))+((7eˆ8-8)/(eˆ8-eˆ3)eˆ(3t))
(correct)
Problem 6. 6. (1 point) Find the stedy-periodic solution xsp
of the Initial value problem
x00 +2x0+5x=5cos(5t),x(0) = 0,x0(0) = 0
xsp =
Answer(s) submitted:
•((1/10)sin(5t))-(1/5)cos(5t)
(correct)
Problem 7. 7. (1 point) A mass m=4 is attached to both a
spring with spring constant k=65 and a dash-pot with damping
constant c=4.
The mass is started in motion with initial position x0=1 and
initial velocity v0=2 .
Determine the position function x(t).
x(t) =
Note that, in this problem, the motion of the spring is un-
derdamped, therefore the solution can be written in the form
x(t) = C1e−pt cos(ω1t−α1). Determine C1,ω1,α1and p.
C1=
ω1=
α1=
(assume 0 ≤α1<2π)
p=
Answer(s) submitted:
•eˆ((-1/2)t)cos(sqrt(128)t-12.46046637)
•1.02412
•sqrt(128)
•12.46046637
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