Oscillation

#m=mass of object (kg) #l=unstretched length of bungee cord (m) #h=height above ground #x=max elongation (from equilibrium) #y=total elongation (elongation from the top) #g=gravitational acceleration (m/s/s) #f=time for free fall (s) #U=initial potential energy (Joules) #E=elastic potential energy (Joules) 

#l=unstretched length of bungee cord (m) #g=gravitational acceleration (m/s/s) **assume positive and constant #f=time for free fall (s) #Find the time it takes to undergo the free fall #Δl=Vit+.5gf^2 #Since Vi=0 #l=.5gf^2 #f=(2l/g)^.5 l=11 g=9.8 f=(2*l/g)^.5 f 

1.49829835452879

1.49829835452879

#Find the spring constant (k) of the bungee cord #KEi+PEi=KEf+PEf #We could use kinematics to find the kinetic energy but the initial potential energy is the same as the potential spring energy because the kinetic energies at those points are equal to zero and there is no outside work besides gravity being done on the system (assuming air resistance and friction are negligible) #0+U=0+E #U=m*g*h #E=.5*k*x^2 #y=total elongation (elongation from the top)=height above ground-unstretched length h=36 l=11 m=65 y=h-l k=(2*m*g*h)/(y^2) k 

73.3824000000000

73.3824000000000

#Find the equilibrium point (o) of the subsequent oscillation #x=elongation (from the equilibrium point #Use Hooke's law #Fs=kx #Fg=mg #At any point the equilibrium point there is no net acceleration because the force of gravity is equal to the restoring force of the spring (**Free body diagram) #Fs=Fg ==> kx=mg x=(m*g/k) x 

8.68055555555556

8.68055555555556

#HOWEVER this means that the center of oscillation is (**8.68) meters below the highest point during the oscillation #Since the highest point of oscillation is (**11) meters below the building, the equilibrium position is (**19.68) meters below the building 

#Find the angular frequency (w) of the oscillation #w=(k/m)^.5 w=(k/m)^.5 w 

1.06252529381658

1.06252529381658

#How long will it take to hit the ground? #t=f+(T/2) #Assume t=total time and T=period #w=2*pi*frequency #frequency=1/T T=2*pi.n()*(m/k)^.5 T 

5.91344539630720

5.91344539630720

f=1.49829835452879 T=5.91344539630720 t=f+(T/4) print "The total time of fall is "+str(t)+"s" 

The total time of fall is 2.97665970360559s

The total time of fall is 2.97665970360559s

#If the bungee jumper spots a thief, 50m away in the horizontal direction, running below at a constant velocity of 5 m/s, how long after the thief is spotted, should the jumper jump in order to knock the thief out? d=50 v=5 #WaitingTime=thiefTime-fallTime wT=(d/v)-2.97665970360559 print "The jumper should wait "+str(wT)+"s" 

The jumper should wait 7.02334029639441s

The jumper should wait 7.02334029639441s