Calculating Damping Coefficient for Spring Mass System | Prototype Home Kit

• daesson777
In summary, the conversation discusses designing a prototype home kit for visualizing the effects of vibration on a spring mass system. The system is unforced and damped by air resistance, and the group is looking for an easy way to calculate the damping coefficient. One member suggests a formula using critical damping coefficient, natural frequency, and damped frequency, and another member confirms it. The final formula given is c=2m(ωn-2π/τd ).
daesson777
Hello.

I'm designing a simple prototype home kit for visualising the effects of vibration on various systems. In this case i have a simple spring mass system in compression that will have responses measured by varying initial displacements.

As it stands the system will be unforced, and damped only by air resistance. Does anyone have a relatively easy way for me to work out the damping coefficient from the basic system data - k, m, max amplitude etc?

Much appreciated people.

Ive done this for a free(unforced), damped system. Anyone confirm or dispute?

Where cc is critical damping coefficient, ωn is natural frequency, ωd is damped.

ωd=ωn √(1-(c/cc )^2 )

And
ωd=2π/τd
cc=2mωn

2π/τd =ωn √(1-(c/(2mωn ))^2 )
(2π/τd )^2=〖ωn〗^2 [1-(c/(2mω_n ))^2 ]
(2π/τd )^2=〖ωn〗^2-[(ωn^2 c^2)/(4m^2 ωn^2 )]
(2π/τd )^2=〖ωn〗^2-[c^2/(4m^2 )]
c^2=4m^2 [ωn^2-(2π/τd )^2]

c=2m(ωn-2π/τd )

1. What is a damping coefficient?

A damping coefficient is a parameter that measures the amount of resistance or friction in a system. In the context of a spring-mass system, it represents the amount of energy dissipated through damping, causing the system to eventually come to rest.

2. How is the damping coefficient calculated?

The damping coefficient can be calculated using the equation: c = 2 * m * ωn * ζ, where c is the damping coefficient, m is the mass of the object, ωn is the natural frequency of the system, and ζ is the damping ratio.

3. What is the significance of the damping coefficient in a spring-mass system?

The damping coefficient plays a crucial role in determining the behavior of a spring-mass system. A higher damping coefficient results in a quicker dissipation of energy and a faster return to equilibrium, while a lower damping coefficient leads to oscillations that can persist for a longer time.

4. How does the damping coefficient affect the natural frequency of a spring-mass system?

The damping coefficient and the natural frequency of a spring-mass system are inversely proportional. This means that an increase in the damping coefficient will result in a decrease in the natural frequency, and vice versa.

5. Can the damping coefficient be adjusted in a prototype home kit?

Yes, the damping coefficient can be adjusted in a prototype home kit by changing the design of the system, such as altering the material of the spring or adding additional dampers. It can also be adjusted by changing the parameters of the system, such as the mass of the object or the damping ratio.

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