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Although it can be generalized to accommodate an n-dimensional non-linear state space system, I'll describe for you a 2 dimensional linear state space system as you have posed in your specific example. This way to make matters simpler and more illustrative. For this system, the $B$ vector is a 2 X 1 vector and $b(t)$ is a scalar. The $B$ vector is properly ...


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If you have a rod, there are three different ways you can try to distort it which can give rise to a wave traveling along the rod. you can give the end a quick twist: this will give rise to a torsional wave you can push on the end: this will give rise to a pressure ("sound") wave you can move it from side to side: this will give rise to a transverse wave ...


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Consider the following experiment: A regularly shaped metal rod is fixed at its top to a ceiling (or such like), so it cannot move. At the bottom of the rod we rigidly attach two strong and heavy handle bars, which allow to exert a torque $\tau$ to the rod. As a result of this torque the rod now torsionally deforms, so that the handle bars are now at an ...


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I don't understand why are you basing you r definition as either SISO or MIMO on the dimensionality of $B$. The same physical system (viberating string in your case), can be either SISO or MIMO depending on your configuration. The question of classifying a system as SISO or MIMO depends on your control parameters, and the parameters which you "read out" or ...


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Such a thing is generally possible. You can test this really easy: take a tuning fork without resonator (so really just the fork itself), hit the desk, hold the fork in the air and listen. You will probably hear almost no sound. Now plug your ears, do the same and press the fork root against your forehead. You will see (hear :-) ). Practically, that's a big ...


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You would. The bones in your arms would conduct the vibrations to your ears, though I'm not sure you could really call that hearing. The bones in your ears and near your ears would certainly feel the vibrations, but without some sort of mechanism that changes vibrations in solid matter to sound, you wouldn't exactly hear it. You hands, however, would ...


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The zero-range nuclear interactions felt by neutrons makes free neutrons, outside a nucleus or a neutron star, an excellent implementation of an ideal gas. However a neutron gas is a little unusual since neutron gases mostly are at such low density and pressure that the neutron-neutron interaction is very unlikely to occur before the neutron either decays ...


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All materials have a resonant frequency Well, sort of. In general, complicated structures will have many resonant frequencies where the amplitudes of any oscillations will have local maxima. However, one of the jobs of structural engineers, and I would assume this would apply to aeroplanes too, is to find these frequencies and make sure that either (a) ...


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You say: All materials have a resonant frequency but this is at best an oversimplification. Any system has a set of normal modes and if you apply driving force at a frequency that matches a normal mode then you will get a resonance. However for any system significantly more complicated than a tuning fork there are many normal modes and non-linearities ...


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Well essentially there is no much difference, at least if we are talking of temperature and we mean "average kinetic energy" as we generally do. Why? Because neutrons as "every-day particles" interact via the nucleon-nucleon potential which similarly to the one between molecules, it is repulsive at short distance and atractive at longer distances. Of course ...


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Neutrons interact with each other only via exchange interaction Neutrons interact via the strong and weak forces. At low energies the interaction is principally via the nuclear force, or residual strong force, which derives ultimately from the strong force interactions between quarks. This can be described as an effective force due to the exchange of ...


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I do not know that it has been done before, but I have no doubt there is a difference. What is not clear is if it would be noticeable by human ear. The difference is explained theoretically by the fact that the string will vibrate different with the supporting body. Only in the hypothetical scenario where the string is held by ideally unmovable holders ...


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If power enters in one place and exits in another, then a traveling wave component must exist (otherwise the net Poynting vector across any plane would be zero). If there is no net flow of energy there can be no traveling wave in a steady state solution. Note that it is possible, for a given shape of waveguide, that some frequencies are perfectly reflected ...



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