Bungee Cord Damping and Unstretched Length Calculation

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SUMMARY

The discussion focuses on calculating the damping constant and unstretched length of a bungee cord used in a jump scenario involving an 80 kg individual. The bungee cord reaches a maximum length of 90m at the lowest point of the jump and oscillates to a length of 80m before coming to rest at 50m. The period of small oscillations is given as 6 seconds. The equations used include T=2π√(m/k) for the spring constant and mg=kΔL for the force balance, where ΔL represents the change in length of the bungee cord.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with the concepts of spring constants and damping
  • Knowledge of basic physics equations related to mass, force, and acceleration
  • Ability to manipulate algebraic equations for solving physical problems
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  • Calculate the spring constant using the provided period and mass values
  • Determine the change in length (ΔL) of the bungee cord during oscillation
  • Explore methods for calculating the damping constant in oscillatory systems
  • Research the effects of different damping ratios on oscillation behavior
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Physics students, engineers, and anyone interested in the mechanics of oscillatory systems and bungee jumping dynamics.

aks_sky
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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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