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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(1):101-121; doi:10.1093/qjmam/10.1.101
© 1957 by Oxford University Press
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THE PERIODIC SOLUTIONS OF THE DIFFERENTIAL EQUATION OF A RESISTANCE-CAPACITANCE OSCILLATOR

A. W. GILLIES

( Northampton Polytechnic London )

A third-order differential equation is considered of a form which arises in con-nexion with a resistance-capacity oscillator, the equation being normalized to the form

where {varepsilon} and µ are small parameters which in the main part of the discussion are re-lated by {varepsilon} = µ2, and g(D) is a particular polynomial operator of the third degree.

The procedure previously applied to a second-order equation with unsymmetrical non-linear damping, is usexd to obtain the periodic solutions having the period of the forcing term when {omega} is near to 1, i.e. for the case of fundamental resonance. It is shown that the resonance curves are of the same form as those obtained for the second-order equation and that the stability of the periodic solutions is determined by variational equations which are likewise identical in form to those previously obtained for the second-order equation.


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