What is Damped harmonic oscillator: Definition and 51 Discussions

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:






{\displaystyle {\vec {F}}=-k{\vec {x}},}
where k is a positive constant.
If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:

Oscillate with a frequency lower than in the undamped case, and an amplitude decreasing with time (underdamped oscillator).
Decay to the equilibrium position, without oscillations (overdamped oscillator).The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called critically damped.
If an external time-dependent force is present, the harmonic oscillator is described as a driven oscillator.
Mechanical examples include pendulums (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves.

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  1. M

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  2. L

    Modeling the Driven Damped Oscillations in a Material

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  3. M

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    Hello, I have a question regarding Damped Harmonic Motion and I was wondering if anyone out there could help me out? Under normal conditions, gravity will not have an affect on a damped spring oscillator that goes up and down. Gravity will just change the offset, and the normal force equation...
  4. Phantoful

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  5. Allan McPherson

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    Homework Statement An oscillator when undamped has a time period T0, while its time period when damped. Suppose after n oscillations the amplitude of the damped oscillator drops to 1/e of its original value (value at t = 0). (a) Assuming that n is a large number, show that...
  6. Gh. Soleimani

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  7. TheBigDig

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  8. J

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  9. T

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  10. T

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  11. T

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  12. Dusty912

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  13. H

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  14. B

    Relaxation Time in Damped Harmonic Oscillators

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  15. V

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  16. S

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  17. D

    How Does Damping Frequency Influence a Harmonic Oscillator?

    Hi, in this article: http://dx.doi.org/10.1016/S0021-9991(03)00308-5 damped molecular dynamics is used as a minimization scheme. In formula No. 9 the author gives an estimator for the optimal damping frequency: Can someone explain how to find this estimate? best, derivator
  18. M

    Archived Analyzing Power Absorption in a Lightly Damped Harmonic Oscillator

    Homework Statement For a lightly damped harmonic oscillator and driving frequencies close to the natural frequency \omega \approx \omega_{0}, show that the power absorbed is approximately proportional to \frac{\gamma^{2}/4}{\left(\omega_{0}-\omega\right)^{2}+\gamma^{2}/4} where \gamma is...
  19. R

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  20. S

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  21. H

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  22. C

    How Do You Calculate Energy Loss in a Damped Harmonic Oscillator?

    Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...
  23. L

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  24. F

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  25. A

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  26. K

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  27. K

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  28. K

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  29. T

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  30. D

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  31. K

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  33. J

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  34. K

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  35. E

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  36. R

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  37. P

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  38. N

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  39. C

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  40. E

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  41. W

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  42. D

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  44. B

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  45. E

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  46. E

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  47. E

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  48. W

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  49. C

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