Spring Mass System Approximations questions

In summary, the conversation is about the reason for adding 1/3 of the mass of the spring to the total mass in spring mass calculations. The speaker is unsure of why this specific amount is needed and has considered factors such as air friction and internal losses in the spring. They also apologize for posting their question in multiple forums.
  • #1
Ethers0n
27
0
I have been trying to figure out why it's considered a "good" approximation in spring mass calculations to add 1/3 of the mass of the spring to the total mass of the system. I understand the need to add SOME extra mass (other than the mass of the weight added to the bottom of the spring for example) but do not understand why specifically that amount is needed. I've thought about air friction losses and losses internal to the spring, but have still come up with nothing. Any help would be appreciated.

Thanks
 
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  • #2
Please do not post your question to more than one forum at a time.

- Warren
 
  • #3
sorry about that...

I didn't realize there was a specific area just for homework questions. I reposted here after I realized where the parent post should have been.
 

Related to Spring Mass System Approximations questions

1. What is a spring mass system?

A spring mass system is a physical system that consists of a mass attached to a spring. When the mass is displaced from its equilibrium position, the spring exerts a restoring force on the mass, causing it to oscillate back and forth around the equilibrium point.

2. How do you approximate the behavior of a spring mass system?

To approximate the behavior of a spring mass system, we use mathematical models that simplify the system by assuming certain conditions, such as no external forces or damping. These models can be solved using equations of motion, such as Hooke's law and Newton's second law, to determine the position and velocity of the mass at any given time.

3. What are the limitations of spring mass system approximations?

Spring mass system approximations have limitations because they are based on simplifying assumptions. These assumptions may not accurately reflect the real-world behavior of a spring mass system, especially when external forces or damping are present. Additionally, the equations used in these approximations may not hold true for highly nonlinear systems.

4. What factors affect the behavior of a spring mass system?

The behavior of a spring mass system is affected by several factors, including the stiffness of the spring, the mass of the object, the amplitude and frequency of the oscillations, and any external forces or damping. Additionally, the initial conditions, such as the initial position and velocity, can also impact the system's behavior.

5. How can we improve the accuracy of spring mass system approximations?

To improve the accuracy of spring mass system approximations, we can use more complex models that take into account external forces and damping, as well as nonlinear behavior. Additionally, using numerical methods and computer simulations can provide more precise solutions for these systems. Conducting experiments and comparing the results to the approximations can also help improve their accuracy.

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