Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x"- 8x' 8(t-3), x(0) 1, x'(0) = 0. In the following parts, use h(te) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L {a(t)}(s) = b. Obtain the solution a(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 3. x(t) = 8. 8. if 0 < t < 3, if 3 < t < 0.

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x"- 8x' 8(t-3), x(0) 1, x'(0) = 0. In the following parts, use h(te) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L {a(t)}(s) = b. Obtain the solution a(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 3. x(t) = 8. 8. if 0 < t < 3, if 3 < t < 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Oo.122.

Subject  :- Advance Mathematic 

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" - 8x' 8(t-3), x(0) = 1, x'(0) = 0. In the following parts, use h(t - c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L {x(t)}(s) = b. Obtain the solution (t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 3. x(t) = 9- if 0 < t < 3, if 3 < t <∞0.
Transcribed Image Text:Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" - 8x' 8(t-3), x(0) = 1, x'(0) = 0. In the following parts, use h(t - c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L {x(t)}(s) = b. Obtain the solution (t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 3. x(t) = 9- if 0 < t < 3, if 3 < t <∞0.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS