Classical Oscillator Resonance: Understanding & Amplification

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SUMMARY

This discussion clarifies the concept of resonance in classical oscillators, emphasizing that resonance occurs when a system is configured to absorb maximum energy. The amplification of oscillatory motion is a result of consistent energy input at the resonant frequency, which reinforces the oscillation. The conversation also highlights the importance of understanding second-order linear ordinary differential equations (ODEs) with constant coefficients to fully grasp the underlying physics. Practical demonstrations, such as using a pendulum and a knotted handkerchief, effectively illustrate these principles.

PREREQUISITES
  • Understanding of second-order linear ordinary differential equations (ODEs) with constant coefficients
  • Familiarity with the principles of classical mechanics
  • Basic knowledge of oscillatory motion and energy transfer
  • Concept of damping in oscillatory systems
NEXT STEPS
  • Research the mathematical modeling of resonance in classical oscillators
  • Explore practical experiments demonstrating resonance and damping
  • Study the effects of varying frequency on oscillatory systems
  • Learn about energy transfer mechanisms in resonant systems
USEFUL FOR

Students of physics, educators explaining resonance concepts, and anyone interested in the practical applications of oscillatory motion and energy transfer in mechanical systems.

samreen
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for a classical oscillator. i kno when resonance happens. what i don't know is WHAT happens in resonance. and WHY it happens. I am very sketchy bt the details...is resonance happening when the system is oriented or configured to b able to absorb max energy? why the amplification? could u suggest reading material?
 
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Make sure you know how to solve second-order linear ODE with constant coefficients
If not,don't bother to think why
 


ive dun the math...for free, damped and forced. trouble is, it feels like math.not physics. which is what I've asked.
 


not physics. which is what I've asked.

I agree wholeheartedly. a Physicist should be able to explain most things without resort to complicated maths.

Try this: Either as a thought experiment or a real one.

Hang a very heavy weight to act as a pendulum.
Take your handkerchief and tie a knot in the end.
Attack the pendulum with your knotted kerchief by hitting the weight repeatedly with the knot, always in the same direction.

You will find that if you strike at random intervals, the pendulum will scarcely move.
If however you always strike at the same point in the motion of the pendulum the blows will add up and the oscillatory motion will increase.
Eventually you will be able to get a good steady swing going.

This is resonance (at very low frequency so you can see what is happening).
The weight is accepting small packets of energy at its resonant frequency. All these packets are reinforcing one and other so energy transfer is high.
You can also upset the oscillation by striking at the wrong moment - when the pendulum is going towards the knot. Do this enough times and you will slow or stop the oscillation.
If you want to demonstrate damping in this experiment use a piece of sponge rubber on a string. The sponge will introduce damping.
 


thanx guys...makes a load of sense now
 

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