ponjavic
Nov13-06, 01:22 PM
Just started vibrations and having trouble applying energy conservation as a means of finding the natural frequency.
So I know wn=root(k/m) and I know that Tmax=Vmax
the problem is:
In the complete assembly, the top of the float is connected to one end of a uniform bar (mass m and length l) which is freely pivoted at its midpoint, as shown below. Derive an expression for the natural frequency of the complete indicator system.
Hint: use Tmax=Vmax
answer: root(6g/(L(3+m/M)))
I do not really have a clue as how to get the energies.
Thinking that the maximum potential energy Vmax is 1/2*k(x0^2) where x0 is maximum displacement of the cylinder in the water.
Then Tmax is supposed to be 1/2*m(x0*wn)^2 where wn is natural frequency. Something like that. I am missing an I somewhere though as there clearly is rotation in the problem.
Any help?
So I know wn=root(k/m) and I know that Tmax=Vmax
the problem is:
In the complete assembly, the top of the float is connected to one end of a uniform bar (mass m and length l) which is freely pivoted at its midpoint, as shown below. Derive an expression for the natural frequency of the complete indicator system.
Hint: use Tmax=Vmax
answer: root(6g/(L(3+m/M)))
I do not really have a clue as how to get the energies.
Thinking that the maximum potential energy Vmax is 1/2*k(x0^2) where x0 is maximum displacement of the cylinder in the water.
Then Tmax is supposed to be 1/2*m(x0*wn)^2 where wn is natural frequency. Something like that. I am missing an I somewhere though as there clearly is rotation in the problem.
Any help?