Solving Spring Energy: Half Amplitude & Kinetic Energy %

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SUMMARY

In the discussion on solving the energy distribution in an ideal spring system, it is established that at half amplitude, the kinetic energy can be calculated using the principles of energy conservation. At maximum amplitude (A), the potential energy is at its peak, represented by the formula 0.5kx², while kinetic energy is zero. Conversely, at the equilibrium point, kinetic energy reaches its maximum, and potential energy is zero. The key takeaway is that the total energy remains constant, allowing for the calculation of kinetic energy at half amplitude using the relationship Et = Ei, where Et is the total energy and Ei is the initial energy.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants (k)
  • Familiarity with the concepts of kinetic and potential energy
  • Knowledge of energy conservation principles in mechanical systems
  • Ability to manipulate algebraic equations for energy calculations
NEXT STEPS
  • Study the derivation of the potential energy formula for springs: PE = 0.5kx²
  • Learn how to apply the conservation of energy principle in oscillatory systems
  • Explore the concept of amplitude in harmonic motion and its effects on energy distribution
  • Investigate the relationship between velocity and kinetic energy in spring systems
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding energy dynamics in oscillatory systems, particularly those involving springs.

go2cnavy
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For an Ideal spring...At half Amplitude, what % of the energy is kinetic?

I know at A the kinetic energy it instantly zero which makes max potential energy (.5kx^2)

I also know that after released, at the instant passising through the equilibrium point kinetic energy is max and potential energy is zero.

From the energy conservation approach Et = Ei so, .5mv^2 = .5kA^2


I have no clue where to start this problem. Maybe I am making it too difficult
 
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go2cnavy said:
For an Ideal spring...At half Amplitude, what % of the energy is kinetic?

I know at A the kinetic energy it instantly zero which makes max potential energy (.5kx^2)

I also know that after released, at the instant passising through the equilibrium point kinetic energy is max and potential energy is zero.

From the energy conservation approach Et = Ei so, .5mv^2 = .5kA^2


I have no clue where to start this problem. Maybe I am making it too difficult
You know how to calculate the potential energy at full amplitude when it is the total energy. You should also be able to calculate it at half amplitude when it is not the total energy. Any energy that is not potentail energy at half amplitude (or anywhere else) is kinetic energy.
 

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