# Multiple-spring system problem....

• Mike Howard
In summary: The extension spring applies force F2 to each of the moveable members. But the tension in the spring is just F2. Imagine a weight hanging up by a rope. If the tension in the rope is 1N, it applies 1N to the weight and 1N to the support.
Mike Howard
The product I'm working on designing simplifies down to a relatively simple three-spring system, which is easily calculated. Unfortunately our company president is weighing in on the design, and doesn't agree with the calculation, and insists the result is something different (based on a fundamentally wrong assumption). I've outlined the problem with a diagram in the attached PDF. At the bottom there are the two different assumptions which were used to come up with the two different results, any assistance into which theory is correct would be greatly appreciated.

Thanks.

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• spring problem.pdf
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Mike Howard said:
The product I'm working on designing simplifies down to a relatively simple three-spring system, which is easily calculated. Unfortunately our company president is weighing in on the design, and doesn't agree with the calculation, and insists the result is something different (based on a fundamentally wrong assumption). I've outlined the problem with a diagram in the attached PDF. At the bottom there are the two different assumptions which were used to come up with the two different results, any assistance into which theory is correct would be greatly appreciated.

Thanks.
If the system is in static equilibrium, then the forces on the left hand moveable member must be equal and opposite, F1=F2. And similarly for the right hand moveable member, F3=F2. The forces on the fixed member are also equal and opposite, because F1=F3.

tech99 said:
If the system is in static equilibrium, then the forces on the left hand moveable member must be equal and opposite, F1=F2. And similarly for the right hand moveable member, F3=F2. The forces on the fixed member are also equal and opposite, because F1=F3.

Thanks. So based on that the total tension in the extension spring (which is the big debate) is 2x F1, as its being acted on and extended at both ends, correct?

Mike Howard said:
Thanks. So based on that the total tension in the extension spring (which is the big debate) is 2x F1, as its being acted on and extended at both ends, correct?
The extension spring applies force F2 to each of the moveable members. But the tension in the spring is just F2. Imagine a weight hanging up by a rope. If the tension in the rope is 1N, it applies 1N to the weight and 1N to the support.

## 1. What is a multiple-spring system problem?

A multiple-spring system problem is a physics problem that involves analyzing the motion and forces of a system of springs connected in series or parallel. This problem is commonly used to study the behavior of springs in different configurations and can also be applied to other systems with elastic elements.

## 2. How do you solve a multiple-spring system problem?

To solve a multiple-spring system problem, you will need to use equations derived from Hooke's law, which states that the force exerted by a spring is directly proportional to its displacement. You will also need to apply principles of conservation of energy and momentum to determine the motion and forces of the system.

## 3. What are some common assumptions made when solving a multiple-spring system problem?

Some common assumptions made when solving a multiple-spring system problem include assuming that the springs are massless, that there is no friction or air resistance, and that the springs are all connected in a straight line with no slacking or stretching. These assumptions simplify the problem and make it easier to solve.

## 4. How does the arrangement of springs affect the behavior of a multiple-spring system?

The arrangement of springs in a multiple-spring system can greatly affect its behavior. For example, connecting springs in parallel will result in a lower overall stiffness, while connecting them in series will result in a higher overall stiffness. Additionally, the placement of a mass or external force can also impact the system's behavior.

## 5. What real-life applications are there for multiple-spring system problems?

Multiple-spring system problems have many real-life applications, such as in the design of suspension systems for cars, the analysis of structures like bridges and buildings, and the study of musical instruments. They can also be used to understand and predict the behavior of biological systems, such as the movement of joints and muscles in the human body.

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