The damping of a spring is calculated with:
$$[\zeta] = \frac{[c]}{\sqrt{[m][k]}}$$
Where c is the 'viscous damping coefficient' of the spring, according to Wikipedia. m is the mass, k is the spring constant, and zeta is the damping ratio.
How is the value of c calculated though? Is it a constant for the air through which the spring is moving or does it depend on the spring itself?
What data is required to calculate it and how can it be done?
I'm just looking at the oscillation of a spring vertically, and I have data for its decreasing amplitude, and the velocity of the spring at all points.
I have the value of the damping ratio, and I'm trying to find the value of 'c' in order to prove the above equation in an investigation.
There is almost no information about this online.
Best Answer
OK, I will assume you have the under-damped case.
If you continue reading the wikipedia article in question you'll find the solution for a underdamped oscillator writen as $$ x(t) = e^{- \zeta \omega_0 t} (A \cos(\omega_\mathrm{d}\,t) + B \sin(\omega_\mathrm{d}\,t )) $$ with $A$ and $B$ constant.
So, take you data, and plot all the maxima (or minima) as a function of time, fit an exponential {*} to that and $\zeta \omega_0$ pops right out.
If you also need to get $\omega_o$ from the data use $$ \omega_\mathrm{d} = \omega_0 \sqrt{1 - \zeta^2 } $$ where you get $\omega_\mathrm{d}$ by extracting the average period (i.e. time from peak to peak) in the data and noting that the period is $T_d = \frac{2 \pi}{\omega_\mathrm{d}}$.
Now you have two equations for two unknowns, so all you have left is a bit of algebra.
{*} Or plot amplitude versus time on semi-log paper if you are doing this the old-school way. Or plot log(amplitude) versus time on linear--linear graph paper. Then extract the slope.