Damped Oscillations: Does Time Change?

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In damped oscillations, the time for one complete oscillation remains constant, provided that the damping coefficient (γ) and the natural frequency (ω0) are time-independent. The differential equation governing damped oscillations confirms this, as the relationship between angular frequency and the period does not change over time. Therefore, the period of oscillation is not affected by the damping process itself. This conclusion is derived from solving the relevant equations. Overall, the period remains independent of time during damped oscillations.
amit25
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Homework Statement



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

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The Attempt at a Solution

 
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Hi amit25. The differential equation for damped oscillations is:
\ddot{x}+\gamma\dot{x}+\omega_0^2x=0​
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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