# Graphing a spring mass collision with a wall

• chusband
In summary, the conversation is about designing a graph or model for evaluating the "bounce" of a mass behind a spring that collides with a wall. The setup includes a simple spring mass system attached to a wall, and another wall closer to the mass than the spring's free length. The mass is pushed back, compressing the spring completely and then released, impacting the other fixed wall. The mass is expected to bounce multiple times before coming to rest. The question is what approach should be used to graph this response, and whether the setup is for schoolwork. The setup is horizontal and the coefficient of restitution is estimated to be around 0.60 for steel bearings.
chusband
TL;DR Summary
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!

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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.

berkeman said:
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.

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## 1. How do you graph a spring mass collision with a wall?

To graph a spring mass collision with a wall, you will need to plot the position of the mass on the y-axis and the time on the x-axis. The graph will show the displacement of the mass as it collides with the wall and bounces back due to the force of the spring.

## 2. What is the purpose of graphing a spring mass collision with a wall?

The purpose of graphing a spring mass collision with a wall is to visually represent the motion of the mass and understand how the force of the spring affects its displacement. This graph can also help in analyzing the energy transfer during the collision.

## 3. What factors can affect the shape of the graph for a spring mass collision with a wall?

The shape of the graph for a spring mass collision with a wall can be affected by various factors such as the initial velocity of the mass, the stiffness of the spring, the mass of the object, and the angle at which the mass collides with the wall.

## 4. How can you determine the maximum displacement of the mass on the graph?

The maximum displacement of the mass can be determined by finding the highest point on the graph. This point will represent the maximum displacement of the mass from its initial position before the collision.

## 5. Can you use the graph to calculate the force of the spring during the collision?

Yes, the graph can be used to calculate the force of the spring during the collision. The area under the graph represents the work done by the spring, which can be used to calculate the force using the formula F = W/d, where F is the force, W is the work, and d is the displacement.

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