# Equation of motion for MDOF system

• Ikidnapu
In summary, the equation of motion for an MDOF system is a set of differential equations that describe the dynamic behavior of a system with multiple degrees of freedom. It can be derived using Newton's second law of motion and makes assumptions such as linearity, equilibrium, and conservation of energy. The equation of motion can be solved using analytical, numerical, or experimental methods and has applications in structural engineering, mechanical engineering, and aerospace engineering.
Ikidnapu

## Homework Statement

Anyone know how to write a equation of motion for a mdof system like this:

http://img100.imageshack.us/img100/1678/mdofsystem.jpg

If u could explain step by step how to do it, would be great.

Thnaks

Last edited by a moderator:
Start by defining a coordinate for each degree of freedom. Then draw the free body diagram for each of the masses. Then, write Newton's second law for each of those masses. That should get you started.

thanks managed to create something, hope it's right.

## 1. What is the equation of motion for a multi-degree-of-freedom (MDOF) system?

The equation of motion for an MDOF system is a set of differential equations that describe the dynamic behavior of a system with multiple degrees of freedom. It takes into account the mass, stiffness, and damping of each degree of freedom to determine the response of the system to external forces.

## 2. How do you derive the equation of motion for an MDOF system?

The equation of motion can be derived using Newton's second law of motion, which states that the sum of all forces acting on a body is equal to its mass times its acceleration. This is applied to each degree of freedom in the system, resulting in a set of second-order differential equations.

## 3. What are the assumptions made in the equation of motion for an MDOF system?

The equation of motion assumes that the system is linear, the forces acting on the system are in equilibrium, and there is no energy dissipation or external energy input. It also assumes that the system is conservative, meaning that the potential energy is solely dependent on the system's configuration.

## 4. How is the equation of motion solved for an MDOF system?

The equation of motion can be solved using various techniques such as analytical, numerical, or experimental methods. Analytical methods involve solving the differential equations directly, while numerical methods use computer simulations to approximate the solution. Experimental methods involve testing the system and measuring its response to determine the equation of motion.

## 5. What are the applications of the equation of motion for MDOF systems?

The equation of motion is essential in various fields such as structural engineering, mechanical engineering, and aerospace engineering. It is used to analyze the dynamic behavior of structures and systems, design control systems, and predict the response of structures to external forces or vibrations.

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