A damped harmonic oscillator loses 6.0% of its mechanical energy per cycle, (a) By what percentage does its frequency differ from the natural frequency f0 = (1/2π)√(k/m) ? (b) After how many periods will the amplitude have decreased to 1/e of its original value? [Sketch the scenario first]

A damped harmonic oscillator loses 6.0% of its mechanical energy per cycle, (a) By what percentage does its frequency differ from the natural frequency f0 = (1/2π)√(k/m) ? (b) After how many periods will the amplitude have decreased to 1/e of its original value? [Sketch the scenario first]

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.44P: Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped...

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A damped harmonic oscillator loses 6.0% of its mechanical energy per cycle, (a) By what percentage does its frequency differ from the natural frequency f₀ = (1/2π)√(k/m) ? (b) After how many periods will the amplitude have decreased to 1/e of its original value? [Sketch the scenario first]

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