Modelling A Stiff Base With A Mass Spring System

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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
AlephZero
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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.
 

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