Help on Question: A Lightly Damped System Vibrates

In summary, a person is seeking help with a question about a lightly damped system and its period. The question involves finding the period if the damping force is removed. There is a function that describes this and the frequency is dependent on the damping term. The person also mentions knowing the amplitude decreases from 50cm to 5.00mm in half a minute, and suggests contacting them for a more accurate answer.

Hi, iv been struggling with this question for some time now, so i thought if some1 can help on the follwoing quiestion:

Q) A lightly damped system vibrates with a period of 15.0s. In half a minute its amplitude decreases from 50cm to 5.00mm. What would be the period if the damping force were removed?

It takes a bit of work to find their definition of $\omega_0$ here, but this explains the frequency dependence on the damping term of an oscillator. $\omega_0$ is the frequency when no damping is present.

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

There is a fuction describing this.
As far as I can remember,it is A=A(max)*e^(-wt)*cos(wt+...)
Since you know that "In half a minute its amplitude decreases from 50cm to 5.00mm." you can find how much is that "w".But I am not very sure,may I can tell you the accurate one if you contact me at wangkehandsome@hotmail.com later.

1. What is a lightly damped system?

A lightly damped system is a system that has a small amount of damping, or resistance, compared to the amount of energy in the system. This allows the system to vibrate for a longer period of time before coming to rest.

2. How does damping affect the vibration of a system?

Damping affects the vibration of a system by reducing the amplitude and increasing the frequency of the vibrations. This means that the system will stop vibrating sooner and the vibrations will be faster.

3. What is the difference between light damping and heavy damping?

The main difference between light damping and heavy damping is the amount of resistance present in the system. Light damping has a small amount of resistance, while heavy damping has a large amount of resistance. This affects the duration and frequency of the vibrations in the system.

4. How does a lightly damped system behave over time?

A lightly damped system will initially have large amplitude vibrations that gradually decrease over time. The vibrations will also have a higher frequency, meaning they will occur more quickly. Eventually, the system will come to rest due to the small amount of damping present.

5. What are some real-world examples of lightly damped systems?

Some examples of lightly damped systems include a swinging pendulum, a guitar string, or a car suspension system. These systems have a small amount of damping, allowing them to continue vibrating for a longer period of time compared to heavily damped systems.

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