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Consider a second order differential linear periodic equation. The friction coefficient is real positive constant. Some transformation of the solution and its first derivative allow writing two-order differential equations with void friction coefficients. The solutions of these equations are periodic functions or sum of periodic function and an oscillating function with monotone linear increasing amplitude. The second order equation with linear friction is recast as a first order system. The coefficients of the principal fundamental matrix solution of the system are explicit analytical functions.

Simplified Mathieu’s equation with linear friction