The carried work has based on transient vibration response of multiple degrees of freedom (MDOF) system. By this work study of Time–history analysis and prediction of the displacement for excitation has done. For the MDOF system, we have taken the four-storey building to done transient vibration. We establish the equivalent spring-mass system. Transient analysis has done for both Undamped and Damped of the forced system of multiple degrees of freedom (MDOF) system. In the case of the Damped system, we have done three stages of damping, i.e., (1) Underdamped system, (2) Critically damped system, (3) Overdamped system. The time-history graph obtained for two different time stages i.e. 0.001 sec & 0.01 sec with initial time 0.000001 sec. The natural frequency has determined by both theoretical calculation and ANSYS. The whole study of transient vibration makes it possible to predict the damping values that oppose any kind of sudden impact or force vibration, such as blasts, earthquakes and tsunamis. The ANSYS is the modelling and simulation software is used to perform the transient vibration response. The Mode Superposition method is used by ANSYS to calculate the structure response
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