Plane polarized oscilation of a spring

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SUMMARY

The discussion focuses on calculating the mechanical energy (E) of a plane polarized oscillation of a spring with an elastic constant (k), natural width (L = 1 meter), and mass (M = 0.1 kg). The oscillation is described as a pure second harmonic with an amplitude (A = 1 meter) and frequency (Omega) determined by the spring's constants. The total mechanical energy is defined as the sum of kinetic energy (Ekin) and potential energy (Epot), which can be derived from the parameters provided.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Knowledge of mechanical energy components: kinetic and potential energy
  • Familiarity with the properties of springs and Hooke's Law
  • Basic grasp of wave functions, particularly sine functions in oscillations
NEXT STEPS
  • Calculate the frequency Omega using the formula for harmonic oscillators
  • Derive the expressions for kinetic energy (Ekin) and potential energy (Epot) in oscillating systems
  • Explore the implications of varying the elastic constant (k) on the oscillation frequency
  • Investigate the effects of amplitude changes on the total mechanical energy of the system
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of oscillating systems and energy calculations in harmonic motion.

DaTario
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Hi All,

Suppose you have a spring with a given elastic constant k. Its natural width is L = 1 meter and its mass is M = 0.1 kg. Now imagine you put this spring to oscilate, with its ends fixed, forming a pure second harmonic oscilation, plane polarized, with frequency Omega. The amplitude of this oscillation is A = 1 meter also.
How is one to determine the energy E of this system ? (mechanical energy of this system E = Ekin + Epot)

P.S. it seems natural that the frequency Omega is to be determined from the constants I alluded above.

P.S. 2: by second harmonic I mean a sine function between the end points (x = 0 and x = 1) with just one crest and one valley.

Best Regards

DaTario
 
Last edited:
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Best Regards

DaTario
 

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