- #1

ponjavic

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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?