How Is the Constant 'c' Derived in Spring Oscillation Calculations?

In summary, the conversation is about using a table of extension and times for 20 oscillations without a mass on the spring to find the average time for one oscillation. The speaker then plotted a graph to find a trend line and determined that c = 4pi2mspring/k. They are unsure of where this formula comes from and would like a better understanding of it. The link provided explains the concept of effective mass in a spring-mass system.
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ramarlon89
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We have been given a table listing the extension and 3 times for 20 oscillations without the mass on the spring stated. I have used this to find an average time then /20 to find t for 1 oscillation, then plotted a t2/x(extension) graph. I have inserted a trend line to find y=mx+c = y=3.8001x + 0.0292. We have been told that c = 4pi2mspring/k (k=25 N m-1) rearrange so mspring = ck/4pi2 = 0.01849111601kg

My questions is where does the c = 4pi2mspring/k come from, I can't find any reference to it at all, I know my answer is right but I would like an understanding of it instead of just writing c = 4pi2mspring/k as if it's fact. Thanks
 
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FAQ: How Is the Constant 'c' Derived in Spring Oscillation Calculations?

What is the mass of a spring?

The mass of a spring refers to the amount of matter or material that makes up the spring. It is typically measured in grams (g) or kilograms (kg).

How do you find the mass of a spring?

The mass of a spring can be found by using a balance or scale. Place the spring on the balance and wait for it to stabilize. The reading on the balance will give you the mass of the spring.

Can the mass of a spring change?

Yes, the mass of a spring can change. If the spring is stretched or compressed, its mass may change slightly due to the change in its shape and distribution of matter. However, the change in mass is usually negligible and can be ignored for most practical purposes.

What factors can affect the mass of a spring?

The mass of a spring can be affected by the type and amount of material used to make the spring, as well as any external forces acting on the spring. Temperature can also affect the mass of a spring, as some materials may expand or contract with changes in temperature.

Why is it important to know the mass of a spring?

Knowing the mass of a spring is important for various reasons. It can help in determining the strength and durability of the spring, as well as its performance in different applications. The mass of a spring is also a crucial factor in calculating its potential energy, which is important in understanding its behavior and applications in fields such as engineering and physics.

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