UTM a) Solve the following differential equation UTM 5 UTM UTM& UTM G UTM 85 dy + 16y 9e2 UTM d*y - UTM ITM UTM
UTM a) Solve the following differential equation UTM 5 UTM UTM& UTM G UTM 85 dy + 16y 9e2 UTM d*y - UTM ITM UTM
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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Transcribed Image Text:QUESTION 2
& UTM
a) Solve the following differential equation
& UTM
6 UTM
5 UTM
UTM
UTM UTM UTM
Py
+ 16y = 9e2¤
& UTM
d*y
- 8
dx4
UTM2
5 UTM 6
b) An undamped oscillation under the influence of external force is given
UTM
by
UTM
m
dt²
and spring constant k and let w
where x(t) is the displacement at time t. Suppose a spring has mass m
UTM & UTM 5 UT
+ kx = .
&UTM
UTM
F(t) = Focos (wot), where wo 7 w. What type of value k and m
so that the corresponding homogeneous solution is
UTM
UTM
with external force
6 UTM
Tn(t) = A cos(wt) + B sin(wt)?
Hence, by using the method of undetermined coefficients, show that
5 UTM
&UTM
8 UTM & UTM
x(t) = A cos(wt) + B sin(wt) +
Fo
m(w².
"UTM 6
5 UTM & UTM
· cos (wot).
& UTM & UT
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