application. G b. Solve the resulting initial value problem, and plot its solution to confirm that it behaves in the specified manner. N 10. Consider the initial value problem y"+yy' + y = d(t – 1), y(0) = 0, y'(0) = 0, %3D where y is the damping coefficient (or resistance). G a. Let y = . Find the solution of the initial value problem %3D
application. G b. Solve the resulting initial value problem, and plot its solution to confirm that it behaves in the specified manner. N 10. Consider the initial value problem y"+yy' + y = d(t – 1), y(0) = 0, y'(0) = 0, %3D where y is the damping coefficient (or resistance). G a. Let y = . Find the solution of the initial value problem %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Differential equations problem ten
Transcribed Image Text:its
application.
G b. Solve the resulting initial value problem, and plot its
solution to confirm that it behaves in the specified manner.
с.
13. f(
N 10. Consider the initial value problem
y" + yy' + y = &(t – 1),
y(0) = 0, y'(0) = 0,
14. f(
where y is the damping coefficient (or resistance).
G a. Let y = ;. Find the solution of the initial value problem
and plot its graph.
b. Find the time t at which the solution attains its maximum
2.
15. f(
value. Also find the maximum value
of the solution.
16. f(
Gc. Let y = i and repeat parts a and b.
17. Th
d. Determine how tj and y¡ vary as y decreases. What are the
values of tj and
initial va
when
Y = 0?
11. Consider the initial value problem
y" +0.1
y" +yy' + y = k8(t – 1), y(0) = 0, y'(0) = 0,
where k is the magnitude of an impulse at t = 1, and y is the damping
coefficient (or resistance).
Observe
as Proble
1
Find the value of k for which the response has
G a. Let y
a.
a peak value of 2; call this value k1.
1
prol
G
G b. Repeat part (a) for y =
its g
с.
c. Determine how kj varies as y decreases. What is the value of
kj when y = 0?
G 18.
12. Consider the initial value problem
y" +0.1
y"+y = fi(t), y(0) = 0, y'(0) = 0,
(u4-k(1) – u4+k(1)) with 0 < k < 1.
2k
1
Observe
where fr(t) =
as Proble
a. Find the solution y = ø (t, k) of the initial value problem.
b. Calculate lim (t, k) from the solution found in part a.
19. а.
solu
k→0+
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