A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A.  a)At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy? b)What fraction of the total mechanical energy is kinetic if the displacement is 1/2 the amplitude? c)By what factor does the maximum kinetic energy change if the amplitude is increased by a factor of 3?

Principles of Physics: A Calculus-Based Text
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Author:Raymond A. Serway, John W. Jewett
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Chapter12: Oscillatory Motion
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A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A

a)At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy?

b)What fraction of the total mechanical energy is kinetic if the displacement is 1/2 the amplitude?

c)By what factor does the maximum kinetic energy change if the amplitude is increased by a factor of 3?

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