Finding mass of spring from time period.

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SUMMARY

The discussion focuses on determining the mass of a spring (m*) using the formula T^2 = [16{(pi)^2}(R^3)N][M+(m*/3)] / [(r^4)n], where T represents the time period, M is the mass attached to the spring, and m* is the mass of the spring itself. By substituting T=0, the equation simplifies to m* = 3(-M), indicating that the effective mass of the spring is three times the negative of the mass M. The formula's derivation is linked to the kinetic energy of the spring, which is essential for understanding the system's dynamics.

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  • Understanding of harmonic motion and oscillation principles
  • Familiarity with the concept of effective mass in spring-mass systems
  • Basic knowledge of kinetic energy and its relation to mechanical systems
  • Ability to interpret mathematical formulas and graphs in physics
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  • Research the derivation of the effective mass in spring-mass systems
  • Study the principles of harmonic motion and oscillation frequency
  • Explore the relationship between time period and mass in oscillatory systems
  • Examine the role of kinetic energy in mechanical oscillations
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Students and educators in physics, mechanical engineers, and anyone involved in the study of oscillatory systems and spring dynamics.

amk_dbz
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As the title suggests, there is a practical in which we have to find mass of the spring (m*) having a block of mass M attached to bottom, from GRAPH of time period (T)^2 against M.
Here's what the practical handbook says:
T^2= [16{(pi)^2}(R^3)N][M+(m*/3)] / [(r^4)n]
there is no reference to what is N,n,R,r
What they do next is to plug in T=0
therefore, M+(m*/3)=0
=> m*/3=-M
Considering magnitude, m*=3(x intercept)

The last part makes some sense but, where does the formula come from?

Thank you! (Sorry for being messy)
 
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