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.
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
7 answers
there are two unknowns in that equation..how do i solve it?
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.
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.
do you know what would be the value of x?
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.
(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.
Thank you Elena
your B is wrong, 8.3/2*73=0.05685
which would make your time
t=ln7/0.05685=34.23sec
which would make your time
t=ln7/0.05685=34.23sec
1 answer