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If a frictional force damping proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton—Jacobi equation Appell's equation of motion Udwadia—Kalaba equation Koopman—von Neumann mechanics. Compare this result with the theory section on resonance , as well as the "magnitude part" of the RLC circuit.

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Placebo group: The other group took dummy pills (placebo). Both groups also went on a high-fiber, low calorie diet. These were the results of the 12 week study, which was published in The Journal of The American Medical Association (a highly respected scientific journal): Heymsfield, et al.

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