# Report on Damped Oscillation: Amplitude, Applications, Comparisons

• alnywk
In summary, the conversation discusses the topic of damped oscillations and its various applications, such as in car and motorcycle shock absorbers. The conversation also mentions the three categories of damped oscillations - light, critical, and heavy damping - and suggests discussing all three types in the report. An example of damping in engineering - the Millennium Bridge project in London - is also mentioned. The conversation concludes with a book recommendation for further insight on the topic.
alnywk
i am going to write a report about damped oscillation .
as i planned , i will discuss the amplitude decays exponentially with time , application .
but that are too little to talk to
then what things need to be further discuss?
and one question if i use one small card and bid card to damp the oscillation , then wt the result will i get ?

I'm struggling to understand exactly what you are asking, but if you want an example where damping is used, think about car and motorcycle shock absorbers. I race motorcycles, and getting the damping right is essential!

I'm not sure what you mean about the card, but if you use a big piece of card as an 'air damper' it will stop the oscillations quicker than a small piece.

For an interesting example of damping in engineering - look up the 'Millenium Bridge' project in London. This public walkway crossing the Thames was closed soon after opening as when people walked across it, they set up resonant frequencies and the whole thing started to move quite alarmingly. To fix the problem, enormous dampers were applied to the bridge to damp out the oscillations.

Hope this helps...

Damped oscillations fall under three categories;

- Light damping - In this case the solution is oscillatory with an exponentially decaying amplitude.
- Critical damping - The solution in this case is an exponential decay. Critical damping is the amount of damping that eliminates the vibration in the shortest possible time.
- Heavy damping - The solution here is the sum of two exponentials.

If you are talking about damped oscillations, I think you ought to discuss all three types of damping, not just the lightly damped case.

'Physics of Vibrations and Waves' by Pain has an in-depth analysis of damped simple harmonic motion and could provide further insight for your talk.

Claude.

## 1. What is a damped oscillation?

A damped oscillation refers to a type of motion where a system, such as a spring or pendulum, experiences a decrease in amplitude over time due to the presence of an external dissipative force. This force causes the system to gradually lose energy and eventually come to rest.

## 2. How is amplitude related to damped oscillations?

Amplitude refers to the maximum displacement of a system from its equilibrium position. In the case of a damped oscillation, the amplitude gradually decreases over time due to the presence of a dissipative force. This decrease in amplitude is known as damping and is a characteristic feature of damped oscillations.

## 3. What are some common applications of damped oscillations?

Damped oscillations have various applications in both science and engineering. Some common examples include shock absorbers in cars, vibration dampers in buildings, and damping mechanisms in musical instruments. Damped oscillations are also used in seismology to study earthquake waves and in electronics to regulate voltage fluctuations.

## 4. How do damped oscillations compare to other types of oscillations?

Damped oscillations differ from other types of oscillations, such as simple harmonic motion, in that they experience a decrease in amplitude over time due to the presence of a dissipative force. This makes their motion less periodic and more gradual compared to other types of oscillations.

## 5. Can damped oscillations occur in nature?

Yes, damped oscillations occur in various natural phenomena such as the swinging of a pendulum, the motion of a boat on water, and the vibrations of leaves on a tree. In nature, there is always some form of damping present, whether it be due to air resistance, friction, or other dissipative forces.

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