Are all damped oscillations periodic?

In summary, there are types of damped oscillation where the time period is not constant and the motion is not periodic. This includes free damped harmonic oscillators in the strongly damped or critically damped regime, as well as undamped harmonic oscillators with irrational frequency ratios that exhibit quasi-periodic motion.
  • #1
Himanshu_6174
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I know the equation for damped oscillation where the damping force depends on velocity. In that case the damped oscillation has a fixed angular frequency and thus time period! I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not periodic!
 
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  • #2
Himanshu_6174 said:
I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not periodic!
For a free (i.e. non-driven) damped harmonic oscillator in the strongly damped or critically damped regime, the motion is not periodic. It's only periodic in the weakly damped regime.

If you consider a pair of undamped harmonic oscillators, then their phase space dynamics on the torus may display quasi-periodic (but not periodic) motion depending on the (ir)rationality of the ratio of their frequencies. This is probably the simplest example of non-periodic motion.
 
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Related to Are all damped oscillations periodic?

1. What are damped oscillations?

Damped oscillations refer to a type of motion where an object experiences repeated back and forth movements that gradually decrease in amplitude over time. This decrease in amplitude is caused by an external force or friction acting on the object.

2. How do damped oscillations differ from simple harmonic motion?

Simple harmonic motion is a type of motion where an object experiences back and forth movements with a constant amplitude and frequency. In contrast, damped oscillations have a decreasing amplitude over time due to the presence of an external force or friction.

3. Are all damped oscillations periodic?

No, not all damped oscillations are periodic. Periodic motion refers to a type of motion that repeats itself after a certain amount of time. Damped oscillations may eventually stop or reach a constant amplitude, making them non-periodic.

4. How do you calculate the period of a damped oscillation?

The period of a damped oscillation can be calculated by dividing 2π by the frequency of the oscillation. The frequency can be determined by measuring the time it takes for the object to complete one full cycle of oscillation.

5. What factors affect the damping of an oscillation?

The damping of an oscillation can be affected by several factors, including the magnitude of the external force or friction, the properties of the object (such as mass and stiffness), and the medium through which the object is moving (such as air or water).

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