Bungee Cord Damping and Unstretched Length Calculation

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The discussion revolves around calculating the damping constant and unstretched length of a bungee cord used in a jump scenario. An individual weighing 80 kg experiences varying cord lengths during oscillations, with the lowest point reaching 90m and eventually resting at 50m. The period of small oscillations is given as 6 seconds, leading to the use of the formula T=2π√(m/k) to find the spring constant. The participant is uncertain about how to determine the change in length (Delta L) due to the varying lengths of the cord. Clarification on these calculations and alternative methods for finding the damping constant is sought.
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I am a bit confused in this problem.

A person of mass 80 kg takes a bungee jump. At the lowest point of the jump the bungee cord is 90m in length and then at the lowest point of the next oscillation the cord has a length of 80m. when the person does eventually come to rest the length of the cord is 50m. the period of the small oscillations just before the person comes to rest is 6s. find the damping constant for the cord and its unstretched length.


What i tried:

Well i have been given the Period of the small oscillations which is 6s. Now to find the spring constant i use this:
<br /> T=2\cdot\pi\cdot\sqrt{\frac{m}{k}}<br />
And then if use this next equation, The only thing i am not sure about is the Delta L. Since the length of the cord changes in the question.
<br /> mg=k\Delta L<br />

Can someone help me clear up on the rope length and the unstretched part. I am just a but confused. and is there an easier way also to find the damping constant since i will have all the relevant parameters?
 
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anybody know?
 
ok then. thank you!
 
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