why critical damping and over damping doesn't undergo oscillations?
It's the boundary between the two conditions. If you have a machine with this boundary state, and you are "tuning" the oprtating prameters in order to obtain critically damped - well then your system may very well oscillate between the over/under damped conditions while you tune.
To avoid this we invented PID controllers, and techniques to set their parameters so as to avoid this oscillation. Engineers learn about this in their systems and controls classes.
can you explain in a more simple way? i am just a pre-u student. haha. can you expalin this based on simple harmonic motion?
So the simplified version is the following: If you have a damped motion without the harmonic potential, it would eventually stop at some point. This will still be true when you introduce the harmonic potential, with the difference that the force will eventually bring the system to the potential minimum. If the dampening is strong enough that it can take away all of the energy before passing the equilibrium point, then the system is overdamped (if you are at the borderline it is critically damped) and thus you do not get an overshoot - resulting in a non-oscillatory behavior.
You are trying to balance a dynamic system - a system that changes. For example, balance a pencil, tip down, on your fingertip. Maybe you can do this, but your fingertip will be constantly moving, reacting to the slight changes in the pencil's balance.
Bicycle riders maintain stability through counter-steering - an experienced rider does it "automatically"; beginners have trouble, and tend to fall over.
The PID loop controller stands for corrections Proportional to the error, the Integral (accumulated sum over time) of the error, and Differential (rate of change) in the error. A PID controller which responds with a correction that is proportional to the error will tend to oscillate, hence the need for the other terms.
For a very mechanical example look at mechanical governors:
your explaination is really informative ! i read a lot of online notes but stiil cant understand.
If something is vibrating in simple harmonic motion, the amplitude of the vibrations depends of the amount of energy in the system. If there is no damping, the vibrations would continue "for ever" at the same amplitude.
Damping takes energy out of the vibrating system and converts it into some other form. For example if you pluck a guitar string, the energy is converted into sound (motion of the air) and the string stops vibrating after a short time.
A guitar string will probably do hundreds of oscillations before all the energy is gone and the vibration stops. If the amount of damping is higher, the energy is taken out quicker and the vibration stops sooner.
"Critiical damping" is when the energy is taken out so fast that the system doesn't even complete one cycle of "vibration" before it stops.
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