Amplitude and frequency - mass is problem to keep them independent of each other
Facts – Simple harmonic motion is
one ideal theory of oscillation. One of the most important characteristics of
oscillation is supposed to be the independence of amplitude and time period. Or
we can say that amplitude is unaffected by frequency.
We know that mass has character
of inertia and that is why when we explore high values of frequency then
problem we face that speed of particle while passing mean position v = A w, cannot
be greater than speed of light. Mass can
never reach speed of light? So here you
can see that amplitude is creating problem if we want to increase the frequency
of oscillation. We can think about reducing amplitude for high frequency
oscillation. If we are not able to create high frequency of oscillation just by
reducing amplitude, then I can suggest you one more way to do it. You can
reduce mass of particle, along with reducing amplitude, to make high frequency
possible for some material particle. Because mass cannot be moved so quickly
back and forth due to property of inertia associated with mass. One more point
here is to be noted that less amount of energy would be required to generate
high frequency oscillation.
Here everybody can understand
that theory of SHM becomes increasingly applicable if we can keep mass as low
as possible. Maintaining high frequency with large amplitude is possible only
then.
Ok let us keep mass lowest
possible and increase frequency. Now try to increase amplitude a little bit,
then increased speed at mean position will also increase. But remember the
equation of Einstein is not going to allow that you can increase speed of mass
so much. You know it that as per this
equation mass increases with velocity.
How can one drag this equation to
remain part of science knowledge till date?
Why do not people understand this
fact that when mass is somehow pushed to the limit of speed of light then it
gets converted into energy?
Try with light charged particle
to oscillate in electromagnetic field then you will notice mass disappear when
speed at mean position is about to touch the speed of light.
If you oscillate a mass within
appropriate amplitude gap with appropriate frequency then there might be one
luck for humans that mass might appear invisible before it may reach a state of
energy.
Only a massless entity can
perform SHM perfectly. As there will be no conflict in maintaining high
frequencies with even high amplitude. As theoretically zero mass will attain
infinite acceleration to move to any point in no time.
I hope someone is able to
understand the existence of information particle with zero mass. This particle
has no limitation of time to remain anywhere. Because when mass gets associated
then speed decreases.
When you increase the speed of
mass then at high speeds you will notice that mass decreases and finally
disappear when speed increases towards speed of light.
posted by Unknown @ 09:58
3 Comments
3 Comments:
Just notice what happens when you write on a board with chalk. It leaves stain as little amount of matter remains in contact with board and is unable to move along with complete chalk. Here very small force offered by chalk is not sufficient enough to pull back the material left behind.
When some object moves in space then same thing happens with it. Particles in immediate contact with medium particles (air) have a tendency to remain at same location when center of mass is moved. But in most of solid material adhesive force is so strong that we never feel even the spring back action to follow center of mass when they are left behind during motion.
Now just assume mass moving with high speeds then loss of mass due to inertia (induced as friction with surrounding particles) becomes significant. When suppose hypothetically some mass is moving with speed of light then left over mass will never find way to catch up the parent bulk.
Try to forget the equation of einstein described above. It is just confusing everyone to think in right direction.
Visualize there is one rubber like object. And suppose you are oscillating this object by holding from a point. Initially if you keep low frequency then whole mass might appear to move as a single rigid body, but when you increase the frequency then what will happen? Different parts of this object will go out of sync because inter atomic forces would not be able to provide so much force to maintain that acceleration for high frequency. You can do so by increasing energy of oscillation also by keeping same frequency, so that amplitude may become larger. More the object moves away from mean position, then more force would be required for increased acceleration.
Now hold steel object from a point and then start oscillating it using some machinery. When object is away from mean position then it accelerates. Greater distance from mean, indicates greater acceleration. If you are holding some portion of steel body then remaining portion is to be accelerated by interatomic forces only. Suppose acceleration reaches a limit when force required is above minimum force to break it. Then some part will go away.
So property of elasticity is to be considered. Because interatomic forces may not be sufficient to hold integrity of object while oscillating.
Now visualize some very tough object and make some arrangement so that you may put some soft iron type of small object inside some cavity of this object. Now shake object with high frequency, then interatomic forces might surrender and iron might melt, or theoretically you can reach a state of gas also.
Moreover here you should know that maximum required acceleration at extreme is proportional to square of frequency and it is also proportional to amplitude. So frequency will help more to crack the material.
If you are aware of induction furnace then you know that we can put some metal object inside the chamber of induction furnace then turn it on. What happens? Inside furnace magnetic field is changed quickly and randomly to generate eddy currents on the surface of metal body and it gets heated.
Now do one thing that slightly modify the induction furnace. Make the platform where object is kept vibrating, with little high frequency but with very low amplitude and make the platform insulating. Now before putting metal piece inside just charge it using some mechanism. What will happen inside? Shaking charge piece in a highly shaking magnetic field will be trying to do every possible thing. Are you getting me that it will be a total chaos for material. It will melt early. Even if you do not charge the metal then individual free charges will dance to the tune of magnetic field. They will help you to heat the material additionally.
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