how does resonance affect stablity?
79291
Resonance is the ability of a molecule to delocalize a charge. A charge within a molecule is like a "hot potato". If the charged atom can toss the charge around to a couple of its neighbors, it is able to stay in the charged state longer- thus it is more stable. Take for example a carbon with two oxygens attached to it. If one of the oxygens takes on a negative charge it can simply pass the charge to the neighboring oxygen. That oxygen then passes the charge back. The two oxygens simply toss the charge back and forth so that neither oxygen has to hold the charge for too long.
455977
200 Hertz or any integer multiple thereof.\nSo, 400 Hertz, 600 Hz, etc.. would cause it to resonate.
561647
More information needed:\nStanding, sitting, or lying?\nWeight?  Height?  \nDistance between the feet ("stretched wide apart")?\n\nBasically, an object is stable if the center of mass is over the base.  Stability increases with the size of the base and the lowering of the center of mass; i.e., decreasing the ratio of CM height:base.\n\nHope that helps.
268125
just investigate for example ODE y"=-y and then add to the left part increasingly small non-linearity +c*y^2 and find solution of the first order of c - you will see how different modes interact with each other.
1091417
Fascinating question! The surface of the vibrating object would alternately cause reflected light to red shift and blue shift, but that's about as far as my thinking can go. Would the shifts cancel each other, rendering the object invisible?
687884
For any string instrument, like a guitar or piano, the sound comes from each string when is hit  causing the string to oscillate, this oscillation depends on how tense and how long is the string, more tension will cause a higher pith sound, less tension a lower pitch sound.\n\nwhen the string oscillates it transfers the oscillation to air particles that vibrate and create a sound.\n\nThen the resonance box of the guitar, or the piano, gives the vibration a particular effect, by making those vibrations reflect at some distances inside the box.
217085
It may be due to all four casters not being firmly even.  Also, if the floor has any give to it (wooden floor in particular), that can cause it.  Finally, if the load is unbalanced, it will shake no matter how firmly it is sitting.  I had mine shake so bad that it moved across a concrete floor in the basement - finally traced it down to a small drip in the water line above, that made the linoleum floor below wet enough to allow it to move.
888020
For it to be stable, the attraction of the proton has to equal the repulsion of the electrons (the neutrons have no charge). So the electrons have a negative charge, and the protons must counter with an equal positive charge to hold onto those electrons and keep it stable.
627856
Assuming the varible for time is t then the damping ratio is equal to, b(t)/{2*sqrt (k(t) * m(t))}
190160
Better or worse than what? I'm betting this is about a parallel-resonant L-C circuit. I don't know what the original load is, but the more you load down such a circuit (i.e., the lower the load resistance) the broader the resonance and the lower the gain and Q. This follows from a formula for Q, Q=R/sqrt(L/C) (see formula for Q_load in ref.) where w is the resonant frequency (rad/sec), R is resistance and C is capacitance.
83508
If you have ever noticed tread patterns on tires, there will be seemingly random variations in the pitch and withdth of tire sections.  This is to reduce the harmonics of the tire tread on the road and disturb resonant frequencies for a quieter tire.  \n\nPlacing different sized fins on say a lawnmower engine flywheel creates the same effect in the air: it prevents whiny resonances across the RPM range to make a quieter engine and disturb the resonances that would exist otherwise.  \n\nAnother reason there may be different fins is due to the magneto magnet cast into the flywheel.  Some flywheels are composites with a cast aluminum section or a special magnetic section which is attached to the flywheel later on.  The attachments force them to change the fin design in the area of the rivets, or screw castings, or whatever feature they have chosen to mount to the wheel.  Then they must grind a flat opposite the embedded accessory for balancing purposes, which may also include the grinding off of fins in that area as well, causing it too look asymmetrical.  \n\nIf you look at replacement mechanical fan blades for older vehilces you will notice that the fins are not equally spaced.  You might have 3 close together, a wide gap on either side, and then 2 fins directly opposite the three.  This is to control the vibration of the fan and disturb all the resonances to keep the fan safe and keep it from coming apart at certain RPM.  It also makes a quieter fan. \n\nResonances develop in a mass-spring system, which define many rotating assemblies.  If you know the mass of the system and the spring constant, you can calculate the resonant frequency.  This is the point where the driving frequency matches and reinforces the frequency of the mass-spring system, and they continue to amplify the load until the device explodes.  Complex systems have nodes of resonant frequencies, which vary in intensity and value along a frequency band.  \n\nAs an experiment, you can get in your bathtub and close the sliding glass door.  Sing a single note and vary the pitch of that note.  You will notice that some notes become very loud, even though you are not putting more effort into making the sound.  The bathroom walls are forming a cavity of a certain length, and when you hit an even harmonic, the cavity will reinforce the waves and make the sound louder.  This increase in volume is the same increase in energy mass-spring systems encounter when driven at the resonant frequency.\n\nUsually engineers try to make the worst resonant frequency much higher than the assembly will ever see in its use.  For instance, the resonant frequency of an engine may be 10,000 RPM.  They will limit it to 7,000 with a governor to prevent the engine from exploding.
808431
.  Electrical resonance is not generally related to mechanical resonance.  It would be possible, with considerable calculation and inventiveness to put together a device which vibrated in time with or at a harmonic fraction of its electrical resonant frequency, but it would be a real academic undertaking.\n.  There is no single equation to calculate the resonant frequency of "an object".  If you narrowly define the object as say "a taut string" or "a circular plate", equations of only a few terms can be derived for each of those cases, but the equations would not be the same for different cases.  There would be similarities, but they would have diffent constants and different variables.  Most objects would require the development of a complicated mathematical description of the interelatedness of the masses, elastic properties, dimensions, stiffnesses and coupling mechanics of the various components of the object in order to calculate a resonant frequency.  For some complex objects, which are dominated by a single large and simple structure, like say the cylindrical fuselage of an airplane, there are formulae to calculate the resonant frequency.  For objects like suspension bridges, or cable stayed bridges or skyscrapers, it is necessary to go through the pains of developing a mathematical model to find a range within which the object will resonate.  For most objects, you just build it, test it and then do something to eliminate undesirable resonances.\n.  Pretty much the same can be said about calculating the electrical resonance of an object.\n.  For simple resonant circuits there are straightforward formulae for calculating their resonant frequencies, but the formulae are different for different types of resonant circuits.  Whatever text I might have on resonance of electrical circuits is buried in a box somewhere, but should be able to find a book which includes these formuale and other electrical formulae at a college library, online or maybe even at some place like Radio Shack®.
314474
Any  mass-spring system with viscous damping added gives the characteristic quadratic response if the damping force/torque is proportional to velocity. Method to adopt is to draw the block diagram showing the mass-spring system with velocity dependent restraining force as a feedback term.  Block diag gives good visual picture, or you can write eqns of motion down write away if you want.\nAnswer will look something like:         \n  1/(s/wn^2+(2z/wn)*s+1), where wn=undamped natural frequency,\nz is the damping coefficient, and s=j*w in steady- state.\nDamping term will lower the frequency somewhat,and of course z=0.7 is critical damping,no overshoot.
263539
Neutrons can give a nucleus (the core of an atom) stability. They act a little bit like glue to the protons.
90104
If the transistor is stabilized in some circuitry, heat should not affect it too much. A simple amplifier using voltage divider biasing is very stable, whereas simply feeding a signal into the base with the B-E junction forward biased will be very unstable. In the first situation, the stability factor can be made to equal 5. In the second example the stability factor will approximate the beta of the transistor. (Lower S => more stable)
56588
The previous two answers are good, but I might make a couple of comments:\n\n1. This phenomenon is called "sensitive dependence on initial conditions" and it is a common characteristic of nonlinear equations (which in turn are common in the description of the reality around us; for example, the weather). \n\n2. Another term for this sort of behavior is instability, or possibly numerical instability.  \n\nGood luck
734225
i just learned this in class... \nafter you enter your mass matix M,\nyour Dampening Matrix C\nand your Stiffness Matrix K\nyou take [K] - lamda [M]= (b) \nyou can type \n[Evals]=eigs(new)\nThese will also be the square of your natural frequencies.\nyour mode shapes are the eigvectors! fyi