Damped Oscillations: Does Time Change?

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Homework Help Overview

The discussion revolves around the concept of damped oscillations, specifically questioning whether the time for one oscillation changes during the process. Participants are exploring the relationship between angular frequency and the period of oscillation in the context of damping.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the differential equation governing damped oscillations and consider how to derive the angular frequency and its relationship to the period of oscillation. There is a focus on whether this relationship is time dependent or independent.

Discussion Status

Some participants suggest that the period of oscillation may be independent of time, provided certain parameters are constant. There is an ongoing exploration of this idea, with no explicit consensus reached yet.

Contextual Notes

Participants are considering the implications of time-independent parameters such as γ and ω0 in their reasoning about the period of oscillation.

amit25
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Homework Statement



Does the time for one oscillation, change during the damped oscillations? and please explain

Homework Equations





The Attempt at a Solution

 
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Hi amit25. The differential equation for damped oscillations is:
[itex]\ddot{x}+\gamma\dot{x}+\omega_0^2x=0[/itex]​
If you solve for the angular frequency of this system and substitute a relationship between the angular frequency and the period of one oscillation. Is this relationship time dependent or independent? That should give you your answer.
 
so time is independent
 
amit25 said:
so time is independent
The period for one oscillation is independent of the time (as long as γ and ω0 are time independent) if you work out an equation for it.
 

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