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
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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 \(\omega = 1\).
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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