Calculating Damping Coefficient for Spring Mass System | Prototype Home Kit

[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.

 

[daesson777]

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 )