## On the nonlinear vibrations of a particle in the plane |

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16 pages matching **identical springs** in this book

#### Page 76

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### Contents

GENERAL PROCEDURE FOR STABILITY ANALYSIS AND BASIC | 4 |

FORMULATION OF THE PROBLEM | 10 |

SIMILAR NORMAL MODE VIBRATIONS | 13 |

4 other sections not shown

### Common terms and phrases

6-e plane amplitude asymptotically stable degrees of freedom diagram for equation differentiation with respect equating the coefficients equation 4-7 equations of motion equilibrium position exists at least finite Floquet theory hard spring identical linear springs identical springs initial prestress initial stress kinetic energy least one periodic least period linear differential equation linearized variational equations linearly independent modal curve 5-11 non-identical linear springs nonsimilar normal mode normal modal curve normal mode vibrations numerical integration obtained by substituting orbitally stable original length periodic function periodic solution perturbation method Phase plane physical interest plane restrained points can occur region of instability region of physical Regions of stability similar normal modes solution of A-l solution to 4-25 solutions of period spring constant spring force springs with initial stability analysis Stability diagram stability of 4-25 stability of 4-54 stability to instability transition points transition values unbounded solutions various values yg(x