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:

[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.

 

[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.

 

[asteriatic]

Yes, the time for one oscillation can change during damped oscillations. This is because damped oscillations refer to a system that is experiencing a decrease in amplitude over time due to the presence of a dissipative force. As the amplitude decreases, the period of oscillation also decreases, resulting in a shorter time for one oscillation. This can be seen in the equation for damped oscillations, where the period is inversely proportional to the square root of the damping coefficient. Therefore, as the damping coefficient increases, the period decreases, leading to a change in the time for one oscillation. Additionally, the presence of external forces or changes in the system can also affect the period and therefore, the time for one oscillation.