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Old Sep 11th 2017, 09:00 AM   #1
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Damped Oscillations and Natural Frequency

Hello everyone, recently I've learnt that by damping, it is possible to reduce the natural frequency of an object. Therefore, can anyone kindly explain how this works? Why would damping reduce the natural frequency of an object? Thank you very much!
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Old Sep 12th 2017, 09:28 PM   #2
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Originally Posted by Tomato View Post
Hello everyone, recently I've learnt that by damping, it is possible to reduce the natural frequency of an object. Therefore, can anyone kindly explain how this works? Why would damping reduce the natural frequency of an object? Thank you very much!
The natural frequency of a system is the frequency of the system with no damping whatsoever. So its quite wrong to speak of damping reducing the natural frequency of a system. The frequency of a damped system has a different frequency of the un-damped system simply because they are two different systems and there is no reason for them to have the same frequency at all. Consider a pendulum. It has a natural frequency which depends on the strength of the gravitational field that its in as the length of the pendulum. Now put the pendulum in molasses making it a strongly damped system. The pendulum won't even oscillate because the drag force on the pendulum, bob causes it to slow down an stop. If instead there is a small damping then it will still oscillate but there is still an additional force which acts to slow the oscillations from what they would be with no damping whatsoever.
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Old Sep 13th 2017, 02:41 AM   #3
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Good reply, PMB, but I just like to add something.

simply because they are two different systems and there is no reason for them to have the same frequency at all.
This is true but there is also no reason why two entirely different systems can't have the same natural frequency.

This is one condition for resonance to occur between them.


A classic example is the order given to soldiers to 'break step' when marching over a bridge so they don't set up a resonance with the brdge, particularly a light one.
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Old Sep 13th 2017, 06:35 AM   #4
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Originally Posted by studiot View Post
This is true but there is also no reason why two entirely different systems can't have the same natural frequency.
That would be taking what I said out of context since the "entirely different system" I was speaking about is the damped system relative to same but un-damped system.

Regarding marching soldiers. I know this phenomena since I was in the military. When we were ordered to break stride it was in order to reduce the amplitude of the oscillation set up. The stride of a set of marching men isn't necessarily the resonant frequency of the bridge being marched over. But resonance does apply here.

A widely used example of aerodynamics and resonance in physics textbooks (which properly explain it) is the Tacoma Narrows Bridge. See: https://en.wikipedia.org/wiki/Tacoma...s_Bridge_(1940)

Scroll down to see "Resonance (due to Von Kármán vortex street) hypothesis"

Note the difference - https://en.wikipedia.org/wiki/Resonance
In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies.
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Old Sep 13th 2017, 08:53 AM   #5
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Discussing resonance is all very well but off topic since the OP has been told correctly that the period of oscillation of a damped SHM system increases with increasing damping, that is the frequency of oscillation decreases with increasing damping and is therefore a maximum when the damping is zero or absent.

Tomato
The relationship is non linear (it lies on a quarter circle about the origin). Are you up to the maths of comparing the relevant two differential equations of motion as this is the only way I know to explain further?
I will post the maths if you like.
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Old Sep 13th 2017, 10:48 AM   #6
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Originally Posted by studiot View Post
Discussing resonance is all very well but off topic ..
You mentioned it. I merely commented on it.

It's been my experience that when a question such as that asked by Tomato is posted and they knew the math then its likely that he/she would have simply looked it up for him/herself. That's because that level of math is typically learned in college where basic physics is often required reading for those who need to learn that math.

Last edited by Pmb; Sep 13th 2017 at 11:48 AM.
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