Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2. Consider the fourth-order boundary-value problem p''(x) – a*q(x) = 0 p(0) = p'(0) = P(1) = p"(1) = 0 where a > 0. Show that there is a non-trivial solution p(x) if and only if tan a = tanh a. Note: This boundary-value problem arises in modeling the vibrations of a beam that is clamped at one end and simply supported at the other. (See hint for problem 1.)

2. Consider the fourth-order boundary-value problem p''(x) – a*q(x) = 0 p(0) = p'(0) = P(1) = p"(1) = 0 where a > 0. Show that there is a non-trivial solution p(x) if and only if tan a = tanh a. Note: This boundary-value problem arises in modeling the vibrations of a beam that is clamped at one end and simply supported at the other. (See hint for problem 1.)

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
2. Consider the fourth-order boundary-value problem φ '' (*) -α*φ (x) 0 p(0) = p'(0) = 0 φ(1) φ '(1) - 0 .4 where a > 0. Show that there is a non-trivial solution p(x) if and only if tan a = tanh a. Note: This boundary-value problem arises in modeling the vibrations of a beam that is clamped at one end and simply supported at the other. (See hint for problem 1.)
Transcribed Image Text:2. Consider the fourth-order boundary-value problem φ '' (*) -α*φ (x) 0 p(0) = p'(0) = 0 φ(1) φ '(1) - 0 .4 where a > 0. Show that there is a non-trivial solution p(x) if and only if tan a = tanh a. Note: This boundary-value problem arises in modeling the vibrations of a beam that is clamped at one end and simply supported at the other. (See hint for problem 1.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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