# Dampening Oscillation Spring Question

• JoeyBob
In summary, the speaker discusses the concept of critically damped and its implications for the equations w=ib/2m and m=ib/w. They mention needing to find work and suggest using w=0 to solve for m. They also clarify the difference between "damping" and "dampening" and express confusion about finding the amplitude and phase. They mention that the answer is supposed to be 0.614 and question what type of work they are looking for.
JoeyBob
Homework Statement
See attached
Relevant Equations
x(t)=Ae^(i(wt+phi))
Since its critically damped that means k/m=(b/2m)^2, which would mean w=ib/2m. So m=ib/w. My issue now is that I need to find work.

I could put w back into x(t) to get Ae^((-b/2m)t+phi). I guess I could make this Acos((-b/2m)t+phi)). But I am kinda lost at this point. Sure, I could find the amplitude but I don't see how to get phi and if I am even approaching the question the right way. I haven't even used the spring constant after all.

The answer is suppose to be 0.614.

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Ok so w=0 since critically damped, so 0=k-b^2/4m and you solve for m.

On a pedantic point, the word you want is "damping". "Dampening" means "making moist".

JoeyBob said:
My issue now is that I need to find work.
What kind of work are you looking for? Is it work done by the spring on the mass or is it the energy dissipated by the damping force?

## 1. What is a dampening oscillation spring?

A dampening oscillation spring is a type of mechanical spring that is designed to reduce the amplitude of oscillations or vibrations in a system. It does this by converting kinetic energy into heat energy, thereby dampening the motion.

## 2. How does a dampening oscillation spring work?

A dampening oscillation spring works by using friction or fluid resistance to absorb the energy of an oscillating or vibrating system. This reduces the amplitude of the oscillations and helps to bring the system back to its equilibrium position.

## 3. What are some common applications of dampening oscillation springs?

Dampening oscillation springs are commonly used in various mechanical systems to reduce vibrations and oscillations. Some examples include shock absorbers in vehicles, suspension systems in buildings, and anti-vibration mounts for machinery.

## 4. How do you calculate the dampening coefficient of an oscillation spring?

The dampening coefficient of an oscillation spring can be calculated by dividing the force applied to the spring by the velocity of the system. This will give you the ratio of energy dissipated per cycle of oscillation.

## 5. How can I improve the dampening effect of an oscillation spring?

There are a few ways to improve the dampening effect of an oscillation spring. One way is to increase the friction or fluid resistance in the system. Another way is to use multiple springs in parallel, which can help distribute the energy more evenly and reduce the amplitude of oscillations.

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