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Resonance Concept

Hi,
I am confused about the definition of frequency of the driving force? What does it mean?

I think:
Frequency of the driving force: is the frequency at which the driving force is applied per unit time.

while

Natural Frequency: the frequency at which a body vibrates when there is no (resultant external) resistive force acting on it

For example, If we push a small child on a swing. The swing plus child has a natural frequency of oscillation. A small push in each cycle results in the amplitude increasing until the child is swinging high in the air.

Now lets suppose, the natural frequency is 2 in this case. Which means that the child and swing oscillates 2 times per unit time.

Also, if the frequency of the driving force is 2. I think it means that the driving force is applied 2 times per unit time. (i.e. The person pushes the child 2 times per unit time)

Then resonance will happen.

Is my definition and concept fine or does it require rectification? Thanks for helping :smile:


Definitions in my book:
oscillation: a repetitive back-and-forth or up-and-down motion

natural frequency: the frequency at which a body vibrates when there is no (resultant external) resistive force acting on it

Resonance: occurs when the frequency of the driving force is equal to the natural frequency of the oscillating system. The system absorbs the maximum energy from the drive and has maximum amplitude.
(edited 1 year ago)
Sounds good to me
Original post by Phys&Math_Ethan
Sounds good to me


ummm, am I allowed to conclude this?

Frequency of the driving force = Frequency of forced oscillations (As driving force produces forced oscillations in the system)


Frequency of the driving force: is the frequency at which the driving force is applied per unit time.

Frequency of forced oscillations: is the frequency at which forced oscillations occur per unit time
Original post by Sinnoh
If at resonance, yes, but not in general/by definition.


What do you mean by general definition? Why is it not true in general case? @Sinnoh
(edited 1 year ago)
Reply 4
Original post by Infinitetimes
What do you mean by general definition? Why is it not true in general case? @Sinnoh


Nope, I ****ed that up, sorry. You were correct. Damn I'm out of practise.
It is forced harmonic motion so the system is being forced to oscillate at a given frequency. But the amplitude of those oscillations will depend on the natural frequency.

e.g. https://en.wikipedia.org/wiki/Harmonic_oscillator#Sinusoidal_driving_force
(edited 1 year ago)
Original post by Sinnoh
Nope, I ****ed that up, sorry. You were correct. Damn I'm out of practise.
It is forced harmonic motion so the system is being forced to oscillate at a given frequency. But the amplitude of those oscillations will depend on the natural frequency.

e.g. https://en.wikipedia.org/wiki/Harmonic_oscillator#Sinusoidal_driving_force

Why do you think amplitude will depend on the natural frequency? I am just concerned about simple harmonic motion. @Sinnoh
(edited 1 year ago)
Reply 6
Original post by Infinitetimes
Why do you think amplitude will depend on the natural frequency? I am just concerned about simple harmonic motion.


If there is a driving force then it isn't simple harmonic motion, it's forced harmonic motion
Original post by Sinnoh
If there is a driving force then it isn't simple harmonic motion, it's forced harmonic motion


That's fine. But why do you think amplitude will depend on the natural frequency? They didn't tell us that in A-Levels. @Sinnoh
(edited 1 year ago)
Reply 8
Original post by Infinitetimes
That's fine. But why do you think amplitude will depend on the natural frequency? They didn't tell us that in A-Levels. @Sinnoh


that's what happens when you solve the equations of motion for a forced harmonic oscillator - the x(t) solution in the wikipedia link. It depends on both natural and driving frequency (specifically the ratio between them), and the amplitude on there is at its maximum when ω=ω0\omega = \omega_0 and smaller when the difference between them is greater.
Original post by Sinnoh
that's what happens when you solve the equations of motion for a forced harmonic oscillator - the x(t) solution in the wikipedia link. It depends on both natural and driving frequency (specifically the ratio between them), and the amplitude on there is at its maximum when ω=ω0\omega = \omega_0 and smaller when the difference between them is greater.

So the amplitude depends on both the natural and driving frequency?
Original post by Infinitetimes
So the amplitude depends on both the natural and driving frequency?


Ye
Original post by Sinnoh
Ye


You told me this "It is forced harmonic motion so the system is being forced to oscillate at a given frequency. But the amplitude of those oscillations will depend on the natural frequency."

You didn't mention driving frequency.

Anyways now I understand it. Thanks a lot :smile:
Original post by Infinitetimes
You told me this "It is forced harmonic motion so the system is being forced to oscillate at a given frequency. But the amplitude of those oscillations will depend on the natural frequency."

You didn't mention driving frequency.

Anyways now I understand it. Thanks a lot :smile:


Should've added a 'too'
Original post by Sinnoh
Should've added a 'too'


Thanks a lot btw :smile:

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