Geodesic
On Relaxation Oscillations Governed by a Second Order Differential Equation for a Large Parameter and with a Piecewise Linear Function(1)
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 80-91

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This paper deals with the differential equation: ẍ + μF(ẋ) + x = ƒ( X, ẋ, t/Tμ) for μ ≫ 1 where F is a piecewise linear function and f is a periodic function of period μT, where T is to be chosen. It is established that periodic forced vibrations exist in an annular domain R(μ) constructed for the free vibration (ƒ ≡ 0), provided ƒ is not of higher order than Subsequently with ƒ = A cos (2πt/μT *), an asymptotic treatment of the forced vibration problem is carried out, by finding the proper initial conditions and the proper period μT * of f. Finally it is concluded that μT * is close to the period of the free vibration.
DOI : 10.4153/CMB-1983-013-0
Mots-clés : 34-02, 34C25, 4E05 
Anand, K. K. On Relaxation Oscillations Governed by a Second Order Differential Equation for a Large Parameter and with a Piecewise Linear Function(1). Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 80-91. doi: 10.4153/CMB-1983-013-0
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