forced vibration question

Although badly phrased, the question actually touches on two common misunderstandings of the effect of applying force at the natural frequency. At least, if I understand correctly.

1. Where does the energy come from? If we take a very simple system, such as a child on a swing set, we know that it takes a fairly large force to raise them slowly up to a height. Yet we can give tiny pushes of very small force and amplitude and get them up very high, if we push at the natural frequency of the system. What is this magic, that puts more energy into the system, lets us break glasses by singing, etc., etc.?

And the answer is, no magic. It takes the same amount of force, whether it is one big push or a lot of little ones.

1. Why doesn't the amplitude continue to increase without limit? The equations seem to go to infinity at resonance, yet we know we can only push a child to a certain height no matter how long we continue to add energy at the natural frequency.

And the answer is, the simplified equations apply only within the assumptions. Beyond small displacements, you have to use all the terms, and they don't go to infinity.

Of course, this answer is probably completely wrong, and I've understood nothing. I am, after all, an engineer. Be gentle in your refutations.

croock the question was about an external force got it? you are trying to obfuscate *your mistake*

an external *constant force* (in addition to the force that is doing the natural harmonic motion)

**will stop the harmonic motion** because only a changable force with the right timing can *add* amplitude and resonance the orriginal question was about a force that causes resonance a constant force can never increase the amplitude because of the very nature of harminic motion tha needs a changeable force to move the obgect one way and *the opposite way* got it ? professional obfuscator?? other people already told you that above and you ignore it because it proves your being wrong!! (and now the croock demands me to admit i am wrong)

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just a good suggestion and material for thinking.

actually just think abouth the pendulum example that you youself brought !!! it is not accidental there is a lot of intuition in it (even *your intuition* ie subconciencely*) even if you dont notice it !!!!

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btw camn you give us in short the botom physics line that expalines resonance of electrons (and please dont evade the question with your 'spoon feeding' excuse because any sound physics theory or model can be presentedin short - at its main base lines we can be sutisfied by baselines only. TIA Y.Porat

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Yes. Why on earth do you think I missed this? Look at my original post. It contains the phrase "the external force" three times, and two times in response to your *wrong* claim that an external constant force will stop the oscillation.

No, not at all. *You* made a mistake. A constant external force does

*not* stop the oscillation.

Again: even an engineer should know this!

No, that is utter nonsense. An external constant force will only change the equilibrium position around which the oscillation happens. It will in no way stop or damp the harmonic motion. Remember my example with a vertical spring on which the constant external force of gravity acts?

Yes, only a periodic force can increase the amplitude. But how on earth does this imply, in your opinion, that a constant external force *stops* the harmonic motion?

Right. So what? It also does not stop the harmonic motion!

Yes. So what? That changeable force is an *internal* force, so it is entirely irrelevant if the external force is constant, periodic or whatever!

Pot. Kettle. Black.

You really are *totally* deluded. What "other people" (Brian Whatcott) said is that *you* are wrong. I'll quote from his post: "Actually, a constant force would have no effect on the oscillation IMO."

That contradicts you, and supports me!!!

How blind *are* you???

Because you are.

A constant external force does *not* stop the oscillation. It merely shifts the equilibrium position of the oscillation.

Even an engineer should know that!

Why is that a good suggestion? What's your basis for suggesting this?

What has that pendulum example to do with electrons?

Do you mean mesomeric effects, or what?

Nonsense. Many things in physics can not be presented in a short time, but need an elaborate explanation.

BTW, your model can also not be presented in short.

[snip]

Bye, Bjoern

Very interesting point.

It is a fact that a constant force is applied to the orbiting electron (thinking here of the Bohr ground orbit), very well known from the Coulomb equation, and that the oscillation is stable (the amplitude hovers about the calculated Bohr radius).

The real question is "What is using up the energy constantly induced by the constant force ?"

André Michaud

For anyone who remembers differential equations, the following is helpful:

Equation (7) is the general solution to the forced oscillator. I think this is beyond the ken of the OP, though.

Tom Davidson Richmond, VA

Of course the obvious example that you are correct is a spring with a mass attached hanging vertically. It oscillates just fine under the constant force of gravity.

Obviously, Old Man's understanding of the OP's intent was initially contrary to Bjoern's interpretation, but upon re-reading, Old Man now agrees that Bjoern's interpretation is consistent with that intended by the OP.

[Old Man]

"ashok" wrote

I think the crux of the issue stems from the statement "With the same excitation force (and hence with the same input energy)..." The same excitation force does not give the same energy, it depends on the resulting motion.

When force and motion are in line then there is energy input, if the motion is opposite the force then there would be energy taken out of the system. With no motion, there is no energy transfer. Furthermore the amount of energy transfered depends on the velocity during the application of the force so that applying the same force to a slowly moving object imparts less energy than that to a quickly moving object. (Work=F D, Power = F V, where F,D, and V are vectors.)

When you are driving a system off the resonant point, some of the time the force is in line with the motion and part of the time the force is opposite the motion. The net result is that there is no net energy into the system over one cycle and therefore no growth in amplitude. In a resonant condition the sinusoidal force is always in the direction of motion so that the net energy addition over the cycle is positive. This extra energy increases the amplitude, which also means the frequency (and hence maximum velocity) also increases. The next cycle applies the same force to a faster moving system, so the additional energy from that cycle is greater. Theoretically this continues unabated until the amplitude becomes infinite.

it ascillates just fine with the applied of Weight. Gravity is not a force. It is an acceleration. and if you look at the equation for free, undamped motion, force never enters into it, and therefore has no effect on it. w^2=K/M M is entirely independent of gravity.If you recall your basic physics, Mass is "an intrinsic characteristic of matter". The frequency of oscillation for any spring-mass system will be the same on the sun, moon (pick one), Earth, Jupiter, Mars, and anywhere and everywhere in between...

Bzzt. No energy is supplied by the centripetal force to a particle in a centered circular orbit, because there is no motion in the direction of the force. Work done =Force*distance*cos(angle between them). The angle is 90 degrees in this case.

In the case of a non circular orbit there are energy transfers during the course of the orbit, but these merely exchange KE for PE.

And I am 99% sure that electrons are not in orbit in any physical sense, and even if they are you'd never be able to observe it. Heisenberg.

Cheers

Greg Locock

Well, that's exactly the example I already provided in my very first post in this thread. Porat keeps ignoring this. Big surprise.

Bye, Bjoern

Assume a spring mass system without friction. The mass hangs on a spring attached to a reference point (nail). You can induce oscillation in a quiescent system by either a. Jerking upward on the suspension point, or b. Pulling down on the suspended mass and letting go. Now it will oscillate forever at radian frequency = sqrt(K/M) and at the amplitude of translation X for either method.

Realize this is a system for storing energy, so any increment FdX that you introduce will add to the stored value and not be lost. If you are doing this by hand, and want to increase amplitude, you will naturally feel when to apply force, which is when the spring force is strongest.

Most likely you will do this by moving the suspension point. Pulling on the moving mass seems like "cheating".

If you lift the nail when the spring is at maximum extension, your force F will be maximum so FdX will be maximum. If you lift it when the mass is highest and the spring shortest, FdX will be a minimum.

You can take energy out of the system if, when the mass is lowest and spring the longest, you move the nail down suddenly and keep it there, realizing that it is the spring that will be pulling your nail down and thus you will be stealing energy from the system.

Notice that at that time the mass is not moving so its KE is zero. Also notice that the clever thing to do is to move your nail down till the spring is exactly at the extension equal ling mg! So now the whole system has been brought to a halt as if it never vibrated.

Here is where an equation would be appropriate but why bother when it would be lost the in the welter of replies? Essays are a relief now and then, but only now and then!

Mr. Dual Space (If you have something to say, write an equation. If you have nothing to say, write an essay).

Until it stops oscillating.

There is a huge difference between assertions based on reading and solving equations and observing the system in operation.

Even under a vacuum bell, the vertical oscillating eventually stops.

Go to any school lab and give it a try.

André Michaud

Yes, obviously the oscillation stops some time in the future. But that it stops has nothing to do with the constant external force acting on it. It stops because of friction forces.

[snip]

Bye, Bjoern

Correct, in theory. In practice there is a maximum amplitude after which there is failure of the system or dissintegration.

Correct, but not in a causative sense. As soon as you start thinking that one causes the other problems start. Your problems start here. Most cranks think that energy is the cause of amplitude in a forced oscillation. This causal connection cannot be proved.

You are equating force with energy. You ibviously do not know Mechanics. The equations are:

dW = dT, this results from the equation for Work and Newton's 2nd law.

dW = F dot dr

T = m v dot v/2 dT = d(m v dot v/2)

If the force is derived from a potential function V(r), as in the case of a spring-mass system, then:

F(r) dot dr = -dV(r)

The function V(r) is known as potential energy and gives rise to a conservative force field.

So,

dT/dt = F dot v

and

dV/dt = - F dot v

add above eqs and you get conservation of energy dT/dt + dV/dt = 0. Then

d(T + V)/dt = 0 and T + V = constant.

If the is an external force, Fnp, which is called a nonpotential force, then:

d(T+V)/dt = dE/dt = Fnp dot v

This states that the rate at which work is done by the nonpotential or external force, equals the time rate of change of the total energy of the system. As long as the force acts, the energy of the system increases as the time integral of the right hand side, (Fnp dot v), the power input to the system.

The answer was given above, i.e. from the power input into the system (F dot v) integrated over time.

Now, to get to the point. There is a crank's book often advertized in these ng's. He obviously thinks force equals input energy to the system. He presents the same exact "problem" in his book. I recommend to him and to you to study basic Mechanics. There is no mystery in the phenomenal explanations of Mechanics you refer to. The philosophical problems are profound but beyond the issues you raised. Possibly, you may have something else in your mind but cannot state it because you lack the background. Before you can start to raise questions about the philosophical issues that are still present in Mechanics, such as the particle-in-motion picture, you must understand the basic equations which are proven to be valid beyond doubt in the empirical world of perception.

Mike

---------------- arrogant demagogic(young goat) phd learn something about harmonic motion and external forces on it, resonance, amplitude augnmentation energy addition to it etc. and about the specific example of the pendulum that you introduced before you jump in and pretent to teach other people physics

---------- crackpot Y.Porat

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the reason it stops is called damping, which translates to friction, whether externally applied, or due to internal material friction at the molecular level. Damping in steel ( a bar, a spring, whatever) will be on the close order of 2% of critical. In rubber, it is close to 30% or so. Has absolutely nothing to do with external forces. The system will cease operating at pretty much the same number of cycles in a vacuum, at zero gravity conditions. In a forced vibration system,the deflection is a function of: 1/(W^2-w^2 +2zWwi) where W is the natural circular frequency (radians/sec), w is the driving (forcing) circular frequency, z is damping, and i=-1^0.5 obviously, if z=0, then when W=w, the deflection would be infinite. That this is not so is a result of the damping value. Do YOU see an "F" in there anywhere? In order to do a transient, or any other modal analysis, one must first find the natural frequencies of the system. Mass enters into the equations, but FORCE does not. Ever. Not At ALL! And Mass is constant, regardless of gravitational acceleration. Period.

Roger W Guinn, PE Structural Dynamics, loads, and Stress

YAY! A voice of reason exists!

Very cleen and to the point.

But my objection here was to the inuendo of some here who missinform (through ignorance) or simply only partly inform (for no noble reason in my book) young readers who look up at them for expert advice, that such motion can last forever.

I am way past trying to argue with them. I rather tend, when aware of such situations in light of my own knowledge, to air a hint at real experimental results to intice questioning.

André Michaud