Overdamped and critically damped oscillator

Thread starter Aneleh
Start date Sep 30, 2005
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Damped Oscillator

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An overdamped or critically damped oscillator can only cross the origin once due to the nature of their motion. Definitions for 'overdamped' and 'critically damped' involve the system's response to disturbances, where overdamped systems return to equilibrium slowly and critically damped systems return as quickly as possible without oscillating. To analyze this, one should derive the equations of motion for both types of damping and calculate the time it takes to cross the origin. Creating a plot of the oscillator's motion can provide visual insight into the behavior of these systems. Understanding these concepts is essential for studying the dynamics of damped oscillators.

Sep 30, 2005

Aneleh

Can you help me start on this one:
Show that an overdamped or critically damped oscillator can cross the origin at most once.

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Sep 30, 2005

hotvette

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Can you help me start on this one

Do you have definitions for 'overdamped' and 'critically damped'? If so, then it seems to me a prudent course of action would be to get equations of each and calculate the time it takes to cross the origin. A plot might be helpful also.

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