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Consider the following ODE: (1) 6+2c +(1+Ecos 2527) = 0, where &, c<<1 and 21. (4.1) Seek a solution in the form = B(1)
Posted: Fri May 06, 2022 6:26 am
by answerhappygod
- Consider The Following Ode 1 6 2c 1 Ecos 2527 0 Where C 1 And 21 4 1 Seek A Solution In The Form B 1 1 (33.54 KiB) Viewed 36 times
Consider the following ODE: (1) 6+2c +(1+Ecos 2527) = 0, where &, c<<1 and 21. (4.1) Seek a solution in the form = B(1) cost + D(t) sin Qt. (2) (4.2) Upon substitution of (2) into (1), omit small terms involving B, D, CB, and cĎ. (4.3) Omit the non-resonant terms, i.e. terms involving cos 3027 and sin 302r. (4.4) Collect like terms and obtain a set of equations for B(1) and D(1). (4.5) Reduce the set obtained in Part (4.4) to a single equation for D(1) and find its general solution. (4.6) On the basis of the solution obtained in Part (4.5), determine the range of 2 for which parametric resonance occurs in the system.