A certain spring-mass system satisfies the initial value problem. u" +u + u = kg(t), u(0) = 0,u' (0) = 0 where g(1) = u92 (t) – 413/2 (1) and k > O is a parameter. Solve the initial value problem.
A certain spring-mass system satisfies the initial value problem. u" +u + u = kg(t), u(0) = 0,u' (0) = 0 where g(1) = u92 (t) – 413/2 (1) and k > O is a parameter. Solve the initial value problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![A certain spring-mass system satisfies the initial value problem.
u" +u' + u = kg(t), u(0) = 0,4'(0) = 0
where g(t) = ug2 (t) – u 13/2 (t) and k > 0 is a parameter.
Solve the initial value problem.
9.
u(t) = u9/2 (1)h(t
– ) -
U13/2 (t)h(t –)where h(t) = k – ke-8 sin-
13.
V63
63
63
t – ke-t/8
-co-
8
63
8
u(t) = [u9/2 (t) – u13/2 (t)]h(t) where h(t) = k – ke-8
V63
sin-
t – ke
63
V63
-cos
8
-t/8
63
u(t) = u9/2 (t)h(t –-) – u13/2(1)h(t
13.
where h(t)
2
V63
co-
-t + ke'
8
(63
-t/8
-sin-
63
V63
-
= ke
-t/8
u(t) = u9/2 (1)h(t –
9.
) – u13/2 (1)h(t –-
13.
V63
V63
-sin-
63
where h(t) = k – ke
2
V63
-t/8
cos
-t – ke
-1/8
u(t) = [u9/2 (t) – u13/2(t)]h(t) where h(t) = k – ke
V63
t - ke¬t/8 V63
-sin-
V63
-t/8
co-
V63
8
63
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cac1a6-5ad9-4f72-bdd9-21a202e53df4%2F8d3f301d-c3bc-4cea-88b8-cc59997fb26c%2Fiyl32g_processed.png&w=3840&q=75)
Transcribed Image Text:A certain spring-mass system satisfies the initial value problem.
u" +u' + u = kg(t), u(0) = 0,4'(0) = 0
where g(t) = ug2 (t) – u 13/2 (t) and k > 0 is a parameter.
Solve the initial value problem.
9.
u(t) = u9/2 (1)h(t
– ) -
U13/2 (t)h(t –)where h(t) = k – ke-8 sin-
13.
V63
63
63
t – ke-t/8
-co-
8
63
8
u(t) = [u9/2 (t) – u13/2 (t)]h(t) where h(t) = k – ke-8
V63
sin-
t – ke
63
V63
-cos
8
-t/8
63
u(t) = u9/2 (t)h(t –-) – u13/2(1)h(t
13.
where h(t)
2
V63
co-
-t + ke'
8
(63
-t/8
-sin-
63
V63
-
= ke
-t/8
u(t) = u9/2 (1)h(t –
9.
) – u13/2 (1)h(t –-
13.
V63
V63
-sin-
63
where h(t) = k – ke
2
V63
-t/8
cos
-t – ke
-1/8
u(t) = [u9/2 (t) – u13/2(t)]h(t) where h(t) = k – ke
V63
t - ke¬t/8 V63
-sin-
V63
-t/8
co-
V63
8
63
8
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