7. Consider the equation x"+w²x = cos Bt. a) Find the solution when the initial conditions are r(0) = r'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. (b) on
7. Consider the equation x"+w²x = cos Bt. a) Find the solution when the initial conditions are r(0) = r'(0) = 0 when w‡ B. b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B) to write the solution as a product of sines. (b) on
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please do 7 a and b
![0
0.5
1
1.5
Figure 2.9 Plot of the solution r(t):
(c) showing the phenomenon of beats.
2
1
2.5
3
3.5
Find the solution and plot the result.
7. Consider the equation
4
10-3(cos(45t) - cos(55t)) to Exercise
4. Consider a general LC circuit with input voltage Vo sin Bt. If B and the
capacitance C are known, what value of the inductance L causes pure
resonance?
=
5. An undamped spring-mass system with m = 4 and and stiffness k is forced
by a sinusoidal function 412 sin 5t. What value of k causes pure resonance?
6. Consider a spring-mass system with small damping and driven by a cosine
force:
z" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0.
x"+w²x = cos Bt.
a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when
w‡ B.
b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B)
to write the solution as a product of sines.
c) Take w=
55 and B
45 and plot the solution from part (b) on
the time interval [0, 4]. The solution can be interpreted as a high fre
quency response contained in a low frequency amplitude envelope. We](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc10cce41-ef51-4545-a724-9736e236d3b7%2Fb5c94119-c8e9-4ebf-8e70-18497f333e62%2F6hia0of_processed.jpeg&w=3840&q=75)
Transcribed Image Text:0
0.5
1
1.5
Figure 2.9 Plot of the solution r(t):
(c) showing the phenomenon of beats.
2
1
2.5
3
3.5
Find the solution and plot the result.
7. Consider the equation
4
10-3(cos(45t) - cos(55t)) to Exercise
4. Consider a general LC circuit with input voltage Vo sin Bt. If B and the
capacitance C are known, what value of the inductance L causes pure
resonance?
=
5. An undamped spring-mass system with m = 4 and and stiffness k is forced
by a sinusoidal function 412 sin 5t. What value of k causes pure resonance?
6. Consider a spring-mass system with small damping and driven by a cosine
force:
z" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0.
x"+w²x = cos Bt.
a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when
w‡ B.
b) Use the trigonometric identity 2 sin A sin B = cos(A-B) - cos(A+B)
to write the solution as a product of sines.
c) Take w=
55 and B
45 and plot the solution from part (b) on
the time interval [0, 4]. The solution can be interpreted as a high fre
quency response contained in a low frequency amplitude envelope. We
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