Damped Oscillations: Does Time Change?

[amit25]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Sleepy_time]

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.

 

[amit25]

so time is independent

 

[Sleepy_time]

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.