How to Calculate Spring Constant and Weight from Oscillation Frequency?

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SUMMARY

The discussion focuses on calculating the spring constant (k) and the weight (m) of a package oscillating with a frequency of 2 Hz using a spring balance with a scale of 0 to 15 kg. The relevant equation used is T = 2π√(m/k), where T is the period of oscillation. The user realizes that they can substitute known values into the equation to derive both k and m, despite initial confusion regarding the displacement from equilibrium and the application of Hooke's Law.

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  • Understanding of oscillation frequency and period
  • Familiarity with Hooke's Law
  • Basic knowledge of spring mechanics
  • Ability to manipulate algebraic equations
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  • Learn how to derive the spring constant using oscillation frequency
  • Study the relationship between mass and weight in oscillatory systems
  • Explore advanced applications of Hooke's Law in different contexts
  • Investigate the effects of damping on oscillation frequency
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Students in physics or engineering courses, lab instructors, and anyone interested in understanding the principles of oscillation and spring mechanics.

Kavorka
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I am in a lab class that is suppose to cover the content of the lecture, however this week we are doing things in lab we haven't even touched in lecture. I have been able to finish the entire report, however there is an extension problem on the lab that I'm not sure how to solve, because we have never solved these in the past:

The scale of a spring balance that reads from 0 to 15 kg is 12 cm long. A package suspended from the balance is found to oscillate vertically with a frequency of 2 Hz. (a) What is the spring constant? (b) How much does the package weight?

I'm not sure how to factor the spring's length into this because it isn't mentioned what the displacement from equilibrium is, just the natural length. I also know that frequency and period (T) are inverses. From the lab we have the equation:

T = 2pi√(m/k)

I'm not sure what else to use in order to solve for both m and k. I don't think I can use Hooke's Law as we don't have the weight or the position.
 
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Kavorka said:
The scale of a spring balance that reads from 0 to 15 kg is 12 cm long.

How can you make use of this to find k?
 
Oh stupid me I can just plug in numbers with that info. I have it now!
 

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