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The problem of random vibrations Induced Dynamics of Train-Track- Fastening System is of considerable practical interest because each part of fastening system i.e. elastic clip, Liner and pad are modeled as a lumped mass with a linear spring and a viscous damper. The track and fastening system are supported and fixed over sleepers which are laid on an elastic or flexible foundation. It is important to predict vehicle dynamic response using realistic track models. Results obtained from the above will be useful to predict the stress, strain, deflections and fatigue behavior of the fastening system for train on Randomly un even track. The same approach can further be used for general induced response analysis of other flexible vehicles and tracks. Some examples are aircraft in ground Runs like taxi, take off and landing, aircraft operation from carrier decks, automobiles and sea vehicles.