Simple Harmonic Oscillator: Kinetic and Potential Energy Equilibrium

AI Thread Summary
In a simple harmonic oscillator with an amplitude of 0.1 m, the displacement where kinetic and potential energies are equal can be determined using energy conservation principles. The total mechanical energy is constant and is the sum of kinetic and potential energy. At the point of equal energy, each type will be half of the total energy. To find the potential energy at any displacement, the formula U = (1/2)kx^2 can be used, where k is the spring constant and x is the displacement. Understanding these concepts is essential for solving the problem effectively.
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Homework Statement



A simple harmonic oscillator has an amplitude of 0.1 m. At what displacement will its kinetic and potential energies be equal?


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The Attempt at a Solution


I'm trying to figure out how to solve this problem but I'm totally stuck and even don't know how to get started since only the amplitude is known and nothing else. I would be incredible happy, if somebody could help me with this problem.
 
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How do you find potential energy of a harmonic oscillator at any particular displacement?
 

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