# Spring damper system without a mass

• hihiip201
In summary, the forces between the spring and damper in parallel must be zero because the node connecting them has no mass, according to the idealized model used by the professor and textbook. This model is a good approximation for very small masses because in such cases, the net force is negligible when the acceleration is finite. This is similar to a circuit with no resistance, where the voltage is 0 because there is no resistance. In extreme cases, the real-life example will approach or resemble the ideal model.
hihiip201
Hi guys:Imagine a spring and and damper in parallel, connected to the ground on the right, and connected by a node on the left.I never quite understand why it is said that the forces between the two must be zero.According to my professor and the textbook, it is because the node has no mass, so the forces between them has to be zero.

But picturing a real life example where masses are being modeled as node by being relatively small compare to the damp coefficient as well as the stiffness of springs.

How does it tell us that the forces exerted on this mass on both side have to be zero? I mean surely F= ma and if m goes to zero then Fnet = 0. But isn't that under the assumption that a is finite?Also, if a small mass is a node, how should i go about trying to visualizing this? I am trying to think of the "wires" connecting mechanical elements as a whole bunch of connected small masses but that's not very helpful.

to me F is the cause, and a is the effect, when two springs, or a damper and spring connected together in parallel or series I don't think " how forces must be equal". instead I think of "How great the acceleartion have to be"
thank you

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spring damper system without a mass
There is always a mass.
Imagine a spring and and damper in parallel, connected to the ground on the right, and connected by a node on the left.
Springs are usually connected in series to the damper - otherwise, what is the point?
I never quite understand why it is said that the forces between the two must be zero. ... According to my professor and the textbook, it is because the node has no mass, so the forces between them has to be zero.
The book and the professor are talking about an idealized model of a spring+damper, not real life. In this model the spring and all the connectors and everything are idealized massless. The effect of any real masses in the real system are included explicitly as a separate component. Just like a circuit diagram shows zero resistance wires connecting components when we know real wires have some resistance.

Simon Bridge said:
There is always a mass.
Springs are usually connected in series to the damper - otherwise, what is the point?The book and the professor are talking about an idealized model of a spring+damper, not real life. In this model the spring and all the connectors and everything are idealized massless. The effect of any real masses in the real system are included explicitly as a separate component. Just like a circuit diagram shows zero resistance wires connecting components when we know real wires have some resistance.
They are connected in parallel for the sake of throwing us students off?lol
Also I believe a mechanical buffer is essentially a damper and a spring in parallel.
I understand that there are always real masses, but what I'm trying to understand it WHY the model is a good approximation of a very small mass.is it because the net force on a tiny mass is negligible when its acceleration is finite?

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I understand that there are always real masses, but what I'm trying to understand it WHY the model is a good approximation of a very small mass.
The model should always include a mass as a separate component. It is usually labelled "m".

A massless model won't obey the laws of motion.
For instance, the slightest unbalanced force produces infinite acceleration.
I think I need to see the specific example.

This situation is analogous to a circuit with no resistance. The voltage across the wire is 0, because there is no resistance. If the voltage were not 0, then there would be an infinite current that would flow, which would generate a charge imbalance which would set the voltage back to 0.

In the case of the spring, if the force on the spring were not 0, then the spring would have infinite acceleration, and it would instantly jump to an equilibrium position where the force is again 0.

These are idealized situations, so this won't happen in real life.

Khashishi said:
This situation is analogous to a circuit with no resistance. The voltage across the wire is 0, because there is no resistance. If the voltage were not 0, then there would be an infinite current that would flow, which would generate a charge imbalance which would set the voltage back to 0.

In the case of the spring, if the force on the spring were not 0, then the spring would have infinite acceleration, and it would instantly jump to an equilibrium position where the force is again 0.

These are idealized situations, so this won't happen in real life.

When you say the velocity of the spring, which point on the spring are you referring to?

Also, I understand that these are idealized model, but I just think that in some extreme cases of the real life example, it will approach/resemble the ideal model approximations.

Simon Bridge said:
The model should always include a mass as a separate component. It is usually labelled "m".

A massless model won't obey the laws of motion.

That is fairly irrelevant IMO. A model without mass obeys a first order differetinal equation, not a second order one. It's a bit like saying you can't solve the quadratic equation ##ax^2 + bx + c = 0## if ##a = 0##. Of course you can solve it - but not using the standard method for quadratics!

Khashishi said:
This situation is analogous to a circuit with no resistance.
No. With the usual analogy between electrical and mechanical equations, it is equivalent to a circuit with no inductance. People work with circults like that all the time! Electrical resistance is analogous to the damper. Bboth dissipate energy, and they are the only parts of the systems which do that.

hihiip201 said:
Also, I understand that these are idealized model, but I just think that in some extreme cases of the real life example, it will approach/resemble the ideal model approximations.

Exactly. If the inertia forces are neglibible compared with the other forces, the model will behave better numerically if you leave them out completely. Ignoring the fact that the acceleration might be "infinite" is a cleaner solution than trying to include an acceleration that is very large but only exists for a very short time.

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Depends what you are trying to model.

AlephZero said:
Exactly. If the inertia forces are neglibible compared with the other forces, the model will behave better numerically if you leave them out completely. Ignoring the fact that the acceleration might be "infinite" is a cleaner solution than trying to include an acceleration that is very large but only exists for a very short time.

Do we need to make the assumption that a is finite (or not very big) before saying the net force/inertia force is small/0 ?

## 1. What is a spring damper system without a mass?

A spring damper system without a mass is a mechanical system composed of a spring and a damper (also known as a shock absorber) that are connected in series, without the addition of a mass. This system is commonly used in engineering and physics to model the behavior of various systems.

## 2. How does a spring damper system without a mass work?

In a spring damper system without a mass, the spring provides a restorative force that is proportional to the displacement of the system from its equilibrium position. The damper, on the other hand, dissipates energy and reduces the system's oscillations. Together, they create a damped harmonic motion that can be described by a differential equation.

## 3. What are the applications of a spring damper system without a mass?

A spring damper system without a mass has many practical applications, including shock absorbers in vehicles, suspension systems in bridges and buildings, and vibration isolation in machinery. It is also used in modeling and analyzing mechanical systems in various fields such as robotics, aerospace, and automotive engineering.

## 4. How is the behavior of a spring damper system without a mass analyzed?

The behavior of a spring damper system without a mass is typically analyzed using mathematical equations and simulations. It is important to consider the properties of the spring and damper, such as their stiffness, damping coefficient, and natural frequency, as well as the initial conditions and external forces acting on the system.

## 5. What are the advantages of using a spring damper system without a mass?

One advantage of a spring damper system without a mass is its ability to reduce the amplitude of oscillations and dissipate energy, which can improve the stability and performance of mechanical systems. It is also relatively simple and cost-effective to implement compared to other damping methods, making it a popular choice in many engineering applications.

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