Modelling A Stiff Base With A Mass Spring System

In summary, The conversation discusses the modeling of a collision between a moving object and a stationary base using a mass spring system with damping. One suggestion is to use two different spring constants to account for the approaching and separating phases of the collision. The coefficient of restitution can also be used to determine the amount of energy that needs to be removed by softening the spring.
  • #1
pollytree
14
0
Hi all.

I am working on a problem in which I want to model the collision of a moving object, with mass m1, with a stationary base. I have calculated the velocity of the moving object at the instant of collision. I want to model this collision using a mass spring system with damping.

My idea was to model mass m1 on an 'infinitely' stiff spring to represent a stiff base. This would have an initial velocity that I calculated previously. Obviously the equivalent system will not be perfect, but an approximation is fine in this case. The issue I am having is with selecting a suitable damping coefficient.

As the moving mass hits the base there will be some vibration before it becomes stationary, i.e. reaches steady state. Hence there needs to be some damping.

Could anyone provide some indication it what I could do in this situation? I don't really have a feel for what would be a suitable damping coefficient. If it is of any use, I am modelling the collision of two steel objects (chrome-moly to be precise).

Thanks for your help! :)
 
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  • #2
One way to do this is use two different spring constants, one when the objects are approaching each other and a smaller one when they are separating. When you reduce the spring stiffnesss, you remove some of the potential energy stored in the spring,

For a collision of two "eigid" objects you can relate the amount of energy removed to the coefficient of restitution between the bodies. Look at the KE of the bodies before and after the collision, and the difference is what you have to remove by softening the spring.
 

1. What is a mass spring system?

A mass spring system is a physical model used to describe the motion of objects that are connected by springs and have mass. It is often used to analyze the behavior of systems such as mechanical oscillators and vibrating structures.

2. How does a mass spring system work?

A mass spring system works by applying Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This force causes the mass attached to the spring to oscillate back and forth.

3. What is the purpose of modelling a stiff base with a mass spring system?

The purpose of modelling a stiff base with a mass spring system is to understand the dynamic behavior of structures that are attached to a rigid base. This can help engineers and scientists design and optimize structures to withstand external forces and vibrations.

4. What factors affect the behavior of a mass spring system?

The behavior of a mass spring system is affected by several factors, including the stiffness of the spring, the mass of the object attached to the spring, and the damping coefficient which determines the rate of energy dissipation in the system.

5. What are some real-world applications of modelling a stiff base with a mass spring system?

Mass spring systems have a wide range of applications in engineering and science, including analyzing the behavior of buildings during earthquakes, designing car suspension systems, and understanding the dynamics of molecular systems in chemistry and biology.

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