# 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:

F

=

k

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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2. ### Energy loss of damped oscillator

yeah, I don't even know how to start
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5. ### Damped harmonic oscillator for a mass hanging from a spring

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6. ### Approximating Damped Oscillator Time Period and Frequency with Large n

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7. ### A The differential equation of Damped Harmonic Oscillator

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11. ### Damped Harmonic Oscillator and Resonance

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15. ### Relaxation Time in Damped Harmonic Oscillators

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16. ### Damped Driven Harmonic Oscillator.

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18. ### How Does Damping Frequency Influence a Harmonic Oscillator?

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19. ### Archived Analyzing Power Absorption in a Lightly Damped Harmonic Oscillator

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20. ### Correlation function of damped harmonic oscillator

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21. ### Damped harmonic oscillator, no clue

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22. ### Springs in a car (damped harmonic oscillator)

This is a problem I've been trying to solve for quite some time now. Any help would be appreciated. Homework Statement When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring...
23. ### How Do You Calculate Energy Loss in a Damped Harmonic Oscillator?

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24. ### Curve fitting of a damped harmonic oscillator

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25. ### How Does Initial Displacement Affect Different Damped Harmonic Oscillators?

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27. ### Damped harmonic oscillator of spring

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28. ### How to Solve for x(t)/x0 in a Damped Oscillator with Initial Values?

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29. ### A lightly damped harmonic oscillator

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30. ### Damped harmonic oscillator being forced

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31. ### Damped Harmonic Oscillator Using Greens Theorem

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32. ### Simple Damped Harmonic Oscillator with friction

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34. ### Mircocanonical Damped Harmonic Oscillator

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35. ### Coupled damped harmonic oscillator

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36. ### Damped harmonic oscillator and displacement

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37. ### How Do You Solve a Damped Harmonic Oscillator Differential Equation?

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38. ### How damped harmonic oscillator affects period

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39. ### Damped Harmonic Oscillator Fourier Expansion

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40. ### What Are the Two Possible Values of C in a Damped Harmonic Oscillator Equation?

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41. ### Fractional energy in a damped harmonic oscillator

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42. ### Driven Damped Harmonic Oscillator Problem

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43. ### Driven Damped Harmonic Oscillator, f = ma?

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44. ### Finding the Work of a Damped Harmonic Oscillator

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45. ### Damped harmonic oscillator physics

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46. ### Driven, damped harmonic oscillator - with particular solution

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47. ### Lightly Damped Harmonic Oscillator

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48. ### Damped Harmonic Oscillator & Mechanical Energy

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49. ### How to Solve a Damped Harmonic Oscillator Problem?

Hi, I'm having a lot of trouble with a damped harmonic oscillator problem: A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10 N/m), and a damping force (F=-bv). Initially it oscillates with an amplitude of 25.0cm. Because of the damping force, the amplitude falls...
50. ### Damped Harmonic Oscillator Approximation?

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