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

  • #36
haruspex
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##\frac{Ce^{-\Gamma t_0/2}e^{-\Gamma T/4}}{-Ce^{-\Gamma t_0/2}} = 4/-8##

##\Gamma = 0.69##

Like that?
Yes.
 
  • #37
EpselonZero
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So basically, ##\Gamma## is how the system decrease "speed"?
 
  • #38
haruspex
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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.
 
  • #39
EpselonZero
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I love you! Seriously big big thanks

one more thing if you want. ##A(\omega_d) = 2.8## is that correct?
 
  • #40
haruspex
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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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