Pendulum Harmonic Motion Help Needed Asap ( work is shown)

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chazgurl4life
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A bungee jumper with mass 66.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 35.5 s. He finally comes to rest 28.0 m below the level of the bridge.

Calculate the spring stiffness constant of the bungee cord.
N/m

For this part i figured i could solve for period (T) which would be the 35.5 sec /8 whihc is 4.4375 s
and then i used T=2pi* (m/k)^1/2

and with that i thought i could solve for K

that comes out to be ...k=(4pi^2*mass) / T^2

so k=132.3 N/m


Calculate the unstretched length of the bungee cord

I could either use T= 2*PI*(L/G)^1/2


L=(4.4375 s^2 * 9.8)/4*pi^2-4.88 m ...but that's wrong

OR I COULD USE ---f= 1/2*pi *(g/l)^1/2 ...

L=(2.46*g)/f^2=477.69 m


and just solve for L ...rite?

but when i plug everything in i keep getting it wrong
 

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No no no no.

The first part (finding k) was correct. Exactly right. But then you start using other formula to find L simply because they have an L in them.

Here's a hint. You have just found the "k," and you are given a distance and a mass (from which you can find a force). What kind of relationship is there for stretchy things that relates force, distance and a "k" ?
 
ok i know that Force = - kx
could x=length of the bungee cord...

and which would lead me to believe that M*g=force also equals -Kx

so...should i be using 66kg (9.8)=-132.3(x) and solve for x?
 
Yes, you should solve for x, but realize that x is not the unstretched length of the cord.

The x in Hooke's law (F = -kx) refers to the amount by which the spring (or cord) is stretched from its unstretched position.
 
so how do i figure out the unstretched length...now I am confused
 
Make full use of the information provided in the problem statement, namely:
"He finally comes to rest 28.0 m below the level of the bridge."​
 
ok i think i got it...so ...66*9.8=-(132.3)x
X in this case is -4.8 ms.. so if i add that to the 28 meters the unstretched cord should be in length equal to 23.1 meters ...that should be rite