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Two Approaches in the Analytical Investigation of the Spring Pendulum


[ 1 ] Instytut Mechaniki Stosowanej, Wydział Budowy Maszyn i Zarządzania, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.8] Mechanical engineering

Year of publication


Published in

Vibrations in Physical Systems

Journal year: 2018 | Journal volume: vol. 29

Article type

scientific article

Publication language


  • nonlinear dynamics
  • asymptotic method
  • spring pendulum

EN Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.

Pages (from - to)

2018005-1 - 2018005-11


License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Full text of article

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