# How to estimate a spring-mass-damper system's damping ratio?

• aerograce
In summary, the conversation discusses the construction and use of a torsional balance to measure thrust from a propulsion system. The system is modeled as a spring mass damper and the speaker is trying to determine the damping ratio and natural frequency from their experiment results. They are also using the log decrement method to obtain damping data from the measured response. The torsional balance works by rotating around a pivot axis and measuring linear displacement caused by the thrust force. There is some confusion about the plot, which shows displacement over time instead of thrust over time.
aerograce
I have constructed a torsional balance, which basically consists of a torsional spring, and a damper. I model this as a spring mass damper system. And it is used to measure thrust of some propulsion system.

This is how the system looks like. I am just very eager to find out, how to model the damping ratio from the experiment result I have got. Basically I turn on the thruster , and let it fire for certain duration, and then turn off the thruster. I don't see a good step response here because of the flow variation noises from the thruster, but I do see a perfect decaying oscillation curve after I turn off the thruster. I already have the curve fit equation for this decaying oscillation. What should I do to get its natural frequency and damping ratio? Is the systems oscillation frequency after this thruster firing at its damped frequency?

I'm having difficulty understanding what you are doing here . Could you please explain some more about the purpose of your experiments and how that test rig actually works ?

Look up information on the idea of the log decrement to get the damping data from your measured response.

Nidum said:
I'm having difficulty understanding what you are doing here . Could you please explain some more about the purpose of your experiments and how that test rig actually works ?

Sure. This torsional balance is able to rotate around the pivot axis, and the pivot is basically a torsional spring. Thruster is mounted at one side of the torsional balance and the counterweight is used to balance the two arms to make sure it stays in horizontal plane. When thrust force is exerted, the torsional balance will rotate to a certain angle. When it is at steady state, the angle should be fixed and the torsional restoring moment of the torsional spring will be equal to the moment created by the thrust force. Here, instead of measuring angle displacement, I measure linear displacement because the rotational angle is very small.

The plot may look confusing. I am sorry about that. It is actually displacement over time plot instead of thrust over time plot. I am trying to find the damping ratio and natural frequency of the system using the oscillating waves after thruster firing.

Hope this clarifies.

Dr.D said:
Look up information on the idea of the log decrement to get the damping data from your measured response.
Thank you! I am looking it up, seems useful!

## 1. What is a spring-mass-damper system?

A spring-mass-damper system is a mechanical system that consists of a spring, a mass, and a damper. The spring provides a restoring force, the mass represents the object being moved, and the damper dissipates energy. This system is commonly used in engineering and physics to model and analyze the behavior of various systems.

## 2. What is damping ratio in a spring-mass-damper system?

The damping ratio, also known as the damping coefficient, is a dimensionless parameter that describes the level of damping in a spring-mass-damper system. It is defined as the ratio of the actual damping in the system to the critical damping, which is the amount of damping required to bring the system to rest in the shortest possible time without oscillating.

## 3. How do you estimate the damping ratio of a spring-mass-damper system?

The damping ratio can be estimated by measuring the amplitude ratio of two successive peaks of the system's response. This can be done by exciting the system with an input force and recording the displacement of the mass over time. The damping ratio can then be calculated using the logarithmic decrement method or the half-power bandwidth method.

## 4. What factors affect the damping ratio in a spring-mass-damper system?

The damping ratio is affected by several factors, including the material properties of the spring and damper, the mass of the object being moved, and the type of motion (e.g. free or forced). Additionally, the damping ratio can be adjusted by changing the design parameters of the system, such as the stiffness of the spring or the damping coefficient of the damper.

## 5. Why is it important to estimate the damping ratio of a spring-mass-damper system?

Estimating the damping ratio is important for understanding and predicting the behavior of a spring-mass-damper system. It helps engineers and scientists determine the stability, response, and performance of the system under different conditions. Additionally, knowing the damping ratio is crucial for designing and optimizing the system to meet specific requirements and objectives.

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