questions主要会涉及到如下几个大类

Single-degree-of-freedom systems代写; free vibrations;

effect of damping; response to harmonic, periodic and arbitrary excitation代写.

Lagrange’s equations of motion.

Vibrations of multi-degree-of-freedom systems代写. Continuous systems.

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Vibration system is a well-dened subject used in many engineering areas like car suspension systems in dynamic mechanics, beam or bridge designs in civil engineering, RLC circuits in electrical engineering, and etc.

Vibration system is the elemental foundation for many engineering problems and applications. Some detailed problems related to vibration system are listed below:
What is the simplest form of vibration system?
How to solve the vibration system under dierent input forces?
How to simplify the complex real world problem into the simplest form?
(usually the real world problem is complex and the degrees of freedom in the system are coupled)

In engineering, the simplest form of vibration system is the mass-spring-dashpot system, which is a second order dierential equation in math.

The concept of nite element method is to divide the domain of the continuous system into multiple small elements. Then, these multiple small elements can be treated as multiple discrete systems as dened and discussed in previous sections. Each element mass matrix, damping coecient matrix and stiness matrix can be computed accordingly and then an assembly of all elements is proceeded such that
the original continuous system is transformed into an approximated discrete system in the form of equation (1).