Consider the same nonlinear, forced ODE: x + dx + 3x + ax³ = cos(wt) Now, set d = 5, B = 6, a = 0. (a) Write down the solution to this ODE for y = 0. (b) Write down the solution for the periodically forced system with y = 1 and w = 1.
Consider the same nonlinear, forced ODE: x + dx + 3x + ax³ = cos(wt) Now, set d = 5, B = 6, a = 0. (a) Write down the solution to this ODE for y = 0. (b) Write down the solution for the periodically forced system with y = 1 and w = 1.
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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![Consider the same nonlinear, forced ODE:
\[ \ddot{x} + \delta \dot{x} + \beta x + \alpha x^3 = \gamma \cos(\omega t) \]
Now, set \(\delta = 5\), \(\beta = 6\), \(\alpha = 0\).
(a) Write down the solution to this ODE for \(\gamma = 0\).
(b) Write down the solution for the periodically forced system with \(\gamma = 1\) and \(\omega = 1\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6e2f997-9120-4975-9388-a1bc7e4c3a16%2F388ef40b-ba95-4440-84fe-dc51314fd4a5%2Foioc2lr_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the same nonlinear, forced ODE:
\[ \ddot{x} + \delta \dot{x} + \beta x + \alpha x^3 = \gamma \cos(\omega t) \]
Now, set \(\delta = 5\), \(\beta = 6\), \(\alpha = 0\).
(a) Write down the solution to this ODE for \(\gamma = 0\).
(b) Write down the solution for the periodically forced system with \(\gamma = 1\) and \(\omega = 1\).
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