# Measuring the natural frequency of a spring-mass system driving force

• happyparticle
In summary: I'll try to find the amplitude and F_0 and post them when I have them.I'll try to find the amplitude and F_0 and post them when I have them.
EpselonZero said:
##\frac{Ce^{-\Gamma t_0/2}e^{-\Gamma T/4}}{-Ce^{-\Gamma t_0/2}} = 4/-8##

##\Gamma = 0.69##

Like that?
Yes.

So basically, ##\Gamma## is how the system decrease "speed"?

EpselonZero said:
So basically, ##\Gamma## is how the system decrease "speed"?
It's how the transient dies away, allowing the period to be controlled by the driving force. It continues to affect the amplitude.

I love you! Seriously big big thanks

one more thing if you want. ##A(\omega_d) = 2.8## is that correct?

EpselonZero said:
I love you! Seriously big big thanks

one more thing if you want. ##A(\omega_d) = 2.8## is that correct?
That's how it looks on the graph you posted.
I encourage you to try to repeat the path I took: observe that the general equation is the sum of a decaying oscillation and a steady oscillation; deduce the steady oscillation parameters from the right hand part of the graph; subtract the equation for the steady part from the graph as a whole to reveal the transient oscillation; from the period and attenuation of the transient deduce its parameters; recreate the curve in a spreadsheet using the parameters calculated.

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