Question

An 73-kg bungee jumper is enjoying an afternoon of jumps. The jumper's first oscillation has an amplitude of 14 m and a period of 6 s. sprint constant is 80.1 n/m and max speed is 14.7 m/s. Treating the bungee cord as a spring with no damping, calculate each of the following:

the time for the amplitude to decrease to 2 m (with air resistance providing the damping of the oscillations at 8.3 kg/s

Answer 1

Use the formula for an underdamped oscillator than can be found at:
http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

What you call the "sprint constant" is the spring constant of the cord.

Answer 2

there are two unknowns in that equation..how do i solve it?

Answer 3

The question seems to contradict itself. They provide a damping constant but tell you to ignore "spring" damping. Damping is what the problem is all about.
You want the amplitude to decrease by a factor of 1/7, from 14 to 2. The exponential factor in front of the sine term will tell you how long that takes, in terms of the damping constant.

Answer 4

do you know what would be the value of x?

Answer 5

The equation of damped oscillations is
(d2x/dt2) +2•β• (dx/dt) +(ωo)^2•x = 0, where
β =r/2•m = 8.3/2•73 = 0.194
14/2= 7 = Ao/A=Ao/Ao•e^(- β•t) = e^ (β•t),
β•t = ln7
t= ln7/ β = 1.94/0.194 = 10 s.

Answer 6

Thank you Elena

Answer 7

your B is wrong, 8.3/2*73=0.05685
which would make your time
t=ln7/0.05685=34.23sec