Question

Why is laplace transform is preferred for vibration analysis?

Answer 1

This discussion will omit the discrete time Z-transform in view of the specified Laplace transform in the question. However, modern control systems are almost all digital and based on a uniform system state and output sampling interval and generation of successive feedback inputs. Analysis of discrete time systems requires the Z-transform and an understanding of the effects of various simple digital filtering algorithms in the Z-plane. The introduction via the Laplace transform in most controls curricula is for continuity with the mathematics taught in prior courses to make understanding feedback principles easier. Fully general multiple input - multiple output (MIMO) treatment of complex real world systems is introduced in conjunction with discrete time principles and the state space description of the system which leads into controlability, observability, state estimation, Kalman filter and other advanced topics

Answer 2

Answer:

Laplace Transform is often used in solving the free vibration problems of structural beams. ... The first four-order frequency of two-span continuous beams with equivalent span lengths. . Frequencies of two-span continuous beams with inequivalent span lengths.