The mechanical energy of an SHM oscillator:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{{\mathbf{v}}}_{{\mathbf{x}}}}^{{\mathbf{2}}}}$where (1/2)kA^{2} is the total energy E, (1/2)kx^{2} is the potential energy U at a point x, and (1/2)mv_{x}^{2} is the kinetic energy K.

Learning Goal: To learn to apply the law of conservation of energy to the analysis of harmonic oscillators.

Systems in simple harmonic motion, or harmonic oscillators, obey the law of conservation of energy just like all other systems do. Using energy considerations, one can analyze many aspects of motion of the oscillator.

Find the kinetic energy K of the block at the moment labeled B. Express your answer in terms of *k* and *A*.

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