# Solving Mass Spring System Collision ODEs

• Nenad
In summary, according to the question, the motion of the two vehicles should be modeled by an ODE. Conservation of linear momentum should be enough to solve for the position and time of each vehicle.
Nenad
Good day all,

I've got a rather puzzeling question on hand that is part of my Dynamic project. I need to model the collision of two vehicles. Each vehicle is traveling head on to the other, and each one has a spring attached to its front. We can assume that the final velovity after collision is the came for both vehicles. I need to set up an ODE for the system and solve for position vs. time for each vahicle. I have tried this by combining the springs into one spring upon collision but this would not be corrct since the compression of the spring would not give a correct value since there are actually two different springs with fdifferent k's meaning different compressions. If anyone has any help, that would be great.

Regards,

Nenad

If you can "assume that the final velovity after collision is the came for both vehicles." then you are really assuming the two vehicles are locked together aren't you? I don't see that you need to set up and ODE. Conservation of momentum should be enough.

HallsofIvy said:
If you can "assume that the final velovity after collision is the came for both vehicles." then you are really assuming the two vehicles are locked together aren't you? I don't see that you need to set up and ODE. Conservation of momentum should be enough.

The question strictly states that the motion should be modeled by ODE's and that linear momentum cannot be used (even though in hinsight they are the same).

Either way, I found out that the one spring system can be used, but only to model the CM of each vehicle. It cannot be used to determine the amount that each spring on each car will compress. I have a solution to this compression from another question, so I can use it.

Thanks anyways man.

Regards,

Nenad

## What is a mass spring system?

A mass spring system refers to a physical system consisting of a mass attached to a spring, which can oscillate back and forth due to the restoring force of the spring.

## What is a collision in a mass spring system?

A collision in a mass spring system occurs when the mass attached to the spring collides with another object or surface, causing a sudden change in velocity and direction.

## What is an ODE in the context of mass spring system collisions?

In this context, an ODE (ordinary differential equation) is a mathematical equation that describes the motion of the mass in the spring system after a collision has occurred. It takes into account the forces and constraints acting on the mass and calculates its position and velocity at any given time.

## How can ODEs be solved for mass spring system collisions?

ODEs for mass spring system collisions can be solved using numerical methods, such as the Euler method or the Runge-Kutta method. These methods involve breaking down the ODE into smaller, simpler equations and using iterative calculations to approximate the solution.

## What are some real-world applications of solving mass spring system collision ODEs?

Solving mass spring system collision ODEs has many practical applications, such as predicting the motion of objects in a collision, designing shock absorbers for vehicles, and understanding the behavior of molecules in chemical reactions. It is also used in computer simulations for video games and animation.

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