Geodesic
A numerical solution of the differential equation of vibration
Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 177 
Apostol Poceski. A numerical solution of the differential equation of vibration. Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 177 . http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a14/
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     author = {Apostol Poceski},
     title = {A numerical solution of the differential equation of vibration},
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     volume = {20},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a14/}
}
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A numerical solution of the differential equation for the vibration of a system with one degree of freedom is considered. Solution step by step, step by step integration. The higher differentials of the equation are anoximated by the product of the lower differentials. Thus it turns out since the time element is finite. Numerical results show very good accuracy of the applied approach. The solution is stable even in the case of using the debt integration step $\Delta t=T/5$.