1. In solving the beam equation, you determined that the general solution is 1 y = 2x²9₁x²³+x. Given that_y'′(1) = 3 determine 9₁ 12 2. The particular solution xp for x' + 2x' = 4e-³¹ is xp = 9₂e-³t 3. In calculating the Laplace transform L{(t+2) H(1-5)} using the formula L{f(t-a)H(t-a)} = e¯ªsL{f(t)} on the Laplace sheet you calculated that the f(t) referred to in this formula is f(t) = **t +93 5 4. The Laplace transform can be expressed as L{e [qssin(961) + 97cos (** 1)]} s² + 4s +6
1. In solving the beam equation, you determined that the general solution is 1 y = 2x²9₁x²³+x. Given that_y'′(1) = 3 determine 9₁ 12 2. The particular solution xp for x' + 2x' = 4e-³¹ is xp = 9₂e-³t 3. In calculating the Laplace transform L{(t+2) H(1-5)} using the formula L{f(t-a)H(t-a)} = e¯ªsL{f(t)} on the Laplace sheet you calculated that the f(t) referred to in this formula is f(t) = **t +93 5 4. The Laplace transform can be expressed as L{e [qssin(961) + 97cos (** 1)]} s² + 4s +6
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
100%
Questions 1-7 please
![1. In solving the beam equation, you determined that the general solution is
x. Given that y'(1) = 3 determine q₁
4_ = 9₁x²³² + 1/1 x .
y =
6
2. The particular solution xp for x' + 2x' = 4e¯³¹ is xp = q₂e-³1
2-31
3. In calculating the Laplace transform L{(1+2) H(1-5)} using the formula
L{f(t-a)H(t-a)} = eªsL{f(t)} on the Laplace sheet you calculated that the f(t)
referred to in this formula is
f(t) = **t +93
4. The Laplace transform
5
s² + 4s +6
can be expressed as L{e [qssin(961) + 97cos(** t)]}
5. The state-space representation for 2x" + 4x' + 5x = 10e' is
11
D-RJD+R-
=
6. Calculate the eigenvalue of the state-space coefficient matrix
0 1
-7a-2a
using the methods
demonstrated in your lecture notes (Note that a is a positive constant, do not assume values for a). If
your eigenvalues are real and different, let ₁ be the smaller of the two eigenvalues when comparing
their absolute values, for example, if your eigenvalues are -3 and -7, their absolute values are
3 and 7 with 3 < 7 and 2₁ = -3. If your eigenvalues are a complex conjugate pair, let ₁ be the
eigenvalue with the positive imaginary part.
The eigenvalue you must keep is λ₁ =q₁1a + 912 a j
Note that if is real valued that 912 = 0
7. The general solution of a non homogeneous state-space equation is given below. Use the initial
conditions to determine the value of C₁.
[x] = G₁ ² [2] + €₂6-²0 - [1]
C₂e-2j)t
-²5+ [_2 ;] + []
given x(0) = 0, x'(0) = 2
You calculated that C₁ = 913+914 j
Note that if C₁ is a real number that 914 = 0.
8. The specific solution of a state space equation is given below. Express the solution Q
terms of sines and cosines using the Euler representation of the complex exponential.
[i]=0.3je] -0.3je[¹]
You calculated that Q=q1scos(t) +916sin(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc83796e5-c9dd-4410-b2cd-8792a3270d87%2Ff121d974-45dc-45bd-be5f-1ad263ce53ba%2Fs4e25u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. In solving the beam equation, you determined that the general solution is
x. Given that y'(1) = 3 determine q₁
4_ = 9₁x²³² + 1/1 x .
y =
6
2. The particular solution xp for x' + 2x' = 4e¯³¹ is xp = q₂e-³1
2-31
3. In calculating the Laplace transform L{(1+2) H(1-5)} using the formula
L{f(t-a)H(t-a)} = eªsL{f(t)} on the Laplace sheet you calculated that the f(t)
referred to in this formula is
f(t) = **t +93
4. The Laplace transform
5
s² + 4s +6
can be expressed as L{e [qssin(961) + 97cos(** t)]}
5. The state-space representation for 2x" + 4x' + 5x = 10e' is
11
D-RJD+R-
=
6. Calculate the eigenvalue of the state-space coefficient matrix
0 1
-7a-2a
using the methods
demonstrated in your lecture notes (Note that a is a positive constant, do not assume values for a). If
your eigenvalues are real and different, let ₁ be the smaller of the two eigenvalues when comparing
their absolute values, for example, if your eigenvalues are -3 and -7, their absolute values are
3 and 7 with 3 < 7 and 2₁ = -3. If your eigenvalues are a complex conjugate pair, let ₁ be the
eigenvalue with the positive imaginary part.
The eigenvalue you must keep is λ₁ =q₁1a + 912 a j
Note that if is real valued that 912 = 0
7. The general solution of a non homogeneous state-space equation is given below. Use the initial
conditions to determine the value of C₁.
[x] = G₁ ² [2] + €₂6-²0 - [1]
C₂e-2j)t
-²5+ [_2 ;] + []
given x(0) = 0, x'(0) = 2
You calculated that C₁ = 913+914 j
Note that if C₁ is a real number that 914 = 0.
8. The specific solution of a state space equation is given below. Express the solution Q
terms of sines and cosines using the Euler representation of the complex exponential.
[i]=0.3je] -0.3je[¹]
You calculated that Q=q1scos(t) +916sin(t)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
