Consider the following ODE: 0 +2° +(1+scos 2921) = 0, (1) where £,c<<1 and 22-1. (4.1) Seek a solution in the form 0 = B

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Consider The Following Ode 0 2 1 Scos 2921 0 1 Where C 1 And 22 1 4 1 Seek A Solution In The Form 0 B 1 (45.53 KiB) Viewed 24 times

Consider the following ODE: 0 +2° +(1+scos 2921) = 0, (1) where £,c<<1 and 22-1. (4.1) Seek a solution in the form 0 = B(1) cos 21+ D) sin $21. (2) (4.2) Upon substitution of (2) into (1), omit small terms involving B, D, CB, and cD. (4.3) Omit the non-resonant terms, i.e. terms involving cos 32 and sin 3. (4.4) Collect like terms and obtain a set of equations for B(t) and D(1). (4.5) Reduce the set obtained in Part (4.4) to a single equation for D) 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.