Graphing a spring mass collision with a wall

[chusband]

TL;DR

Help determining a way to graph the bounce from a collision between a spring-mass system and a wall.

Hi, I'm looking for help making a graph/model for evaluating the "bounce" of a mass behind a spring that collides with a wall. The setup would include one simple spring mass system that is attached to a wall, and another wall which is closer to the mass than the spring's free length. The mass is pushed farthest back compressing the spring completely and then released. After release, it impacts the other fixed wall. Following this, the mass would theoretically bounce a small amount several times before coming to a rest (if the speed/force of the return is sufficiently high). What approach should I use to graph this response? Any help is greatly appreciated, thanks!

 

[berkeman]

Welcome to the PF.

Vertical or horizontal? Coefficient of restitution of the mass hitting the wall?

Could you please attach a PDF file with a sketch of the setup to help clarify your question?

Also, is this for schoolwork? If so, I can move this thread to the schoolwork PF forums. Thanks.

 

[chusband]

Welcome to the PF.

Vertical or horizontal? Coefficient of restitution of the mass hitting the wall?

Could you please attach a PDF file with a sketch of the setup to help clarify your question?

Also, is this for schoolwork? If so, I can move this thread to the schoolwork PF forums. Thanks.

Thanks for your response! Sorry, I really should've specified that, horizontal. In regards to the coefficient of restitution, I'm not sure how to determine that if this is purely analytical, I don't have any existing results to generate one. The part will likely be some form of steel, and steel bearings appear to bounce with a restitution coefficient of approximately 0.60. However, that is an extremely rough assumption. I added a picture. It's not for schoolwork, just a design problem I'm trying to figure out.