Solving a Mass Spring Damper System with Lagrange Equation

In summary, the person is seeking help with writing the equation of motion for a spring-mass-damper system using Lagrange equation. They have tried using the State Space Approach but encountered an issue with getting the homogenous solution. They also mention a website that may provide additional assistance and plan to repost their question in the homework section.
  • #1
Lelak
5
0
Hello!

I am taking a course in dynamics and have a question about a spring-mass-damper system (see the attached file) that I want to solve using Lagrange equation (see attached file).

I am having trouble writing the equation of motion for this problem. At first I tried doing it the way I would for a system with two masses, connected by springs and dampers. This gave me a system of equations which I then used the State Space Approach on. I set the first mass=0, only to realize that I would not be able to get the homogenous solution this way.

Any help is appreciated! Thank you very much!
 

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  • #2
If this is homework, it would be best to put it in that section where you receive a more thorough response, with some description of where you are actually having a problem. ie finding the kinetic energy, potential energy, the "x" to be used for K1, K2, and C1. Waht have you tried and where are you stuck.

Anyways here is a site that might help you out a bit more, from the University of Ottawa, Ontario, Canada.
http://www.site.uottawa.ca/~rhabash/ELG4152L10.pdf
 
  • #3
256bits said:
If this is homework, it would be best to put it in that section where you receive a more thorough response, with some description of where you are actually having a problem. ie finding the kinetic energy, potential energy, the "x" to be used for K1, K2, and C1. Waht have you tried and where are you stuck.

Anyways here is a site that might help you out a bit more, from the University of Ottawa, Ontario, Canada.
http://www.site.uottawa.ca/~rhabash/ELG4152L10.pdf

Okay, I will repost this under the homework section! Thank you!
 

FAQ: Solving a Mass Spring Damper System with Lagrange Equation

What is a mass spring damper system?

A mass spring damper system is a physical system that consists of a mass (usually represented as a point mass), a spring, and a damper. The mass is attached to one end of the spring and the other end is fixed to a stationary point. The damper is connected to the mass and the other end is fixed to a stationary point as well. The system is used to model the behavior of a wide range of mechanical and electrical systems, such as car suspensions, building vibrations, and electrical circuits.

How does a mass spring damper system work?

In a mass spring damper system, the mass is pulled down by gravity, which causes the spring to stretch. As the spring stretches, it exerts a restorative force on the mass, trying to return it to its equilibrium position. The damper, on the other hand, dissipates energy from the system, reducing the amplitude of the oscillations. This interplay between the forces of the spring and the damper results in a damped harmonic motion of the mass around its equilibrium position.

What factors affect the behavior of a mass spring damper system?

The behavior of a mass spring damper system is affected by several factors, including the mass of the object, the stiffness of the spring, and the damping coefficient of the damper. The initial conditions, such as the initial displacement and velocity, also play a significant role in determining the behavior of the system. Additionally, external forces, such as applied forces or friction, can also impact the system's behavior.

What is the equation of motion for a mass spring damper system?

The equation of motion for a mass spring damper system is a second-order linear differential equation, given by m(d^2x/dt^2) + c(dx/dt) + kx = F(t), where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement of the mass, and F(t) is the external force applied to the system. This equation can be solved using various mathematical techniques to determine the behavior of the system.

What are some real-world applications of mass spring damper systems?

Mass spring damper systems have a wide range of applications in various fields. In mechanical engineering, they are used to model the suspension systems of vehicles, shock absorbers, and vibration isolation systems. In civil engineering, they are used to model the behavior of buildings and bridges under seismic forces. In electrical engineering, they are used to model electrical circuits and electronic filters. These systems are also used in robotics, aerospace engineering, and many other fields.

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