### Abstract

The vibrations of a linear discrete mechanical system of n degrees of freedom are governed in physical space by a matrix differential equation of nth order. This means, in general, the solution of an eigenvalue problem of the dimension n. for n ≥3, the eigenvalue problems can generally be solved only numerically, by means of a computer. Only in special cases it is possible to determine the eigencharacteristics of an eigenvalue problem analytically. a uniform oscillator with n equal masses m and n equal linear springs k is an example. Such a system can be thought of, for example, as a simplified discretized model for the longitudinal vibrations of a clamped-free rod. The aim of the present study is to obtain the displacements of the n masses analytically, when the free end is subjected to a force f(t). Then the responses for special forms of f(t) such as the unit-impulse function, the unit-step function and harmonic excitation, are obtained.

Original language | English |
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Pages (from-to) | 283-288 |

Number of pages | 6 |

Journal | Journal of Sound and Vibration |

Volume | 173 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2 1994 |

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### ASJC Scopus subject areas

- Engineering(all)
- Mechanical Engineering

### Cite this

*Journal of Sound and Vibration*,

*173*(2), 283-288. https://doi.org/10.1006/jsvi.1994.1547