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Exercise:
A damped oscillation hasprv a linear envelope with an initial amplitude AO and a decrease rate of aO. The oscillation frequency is fO. abcliste abc Graph the oscillation until the amplitude has dropped to zero. abc What fraction of the oscillation energy is left after tbO? abcliste

Solution:
abcliste abc The oscillation period is T TF fracf TP The linear envelope can be expressed as At A_ -a t with aaO. The amplitude has dropped to zero when -a t_ Longrightarrow t_ tzF fraca tzP These values result in the following graph: center includegraphicswidthtextwidth#image_path:linear-envelop# center abc The oscillaltion energy is proportional to the square of the amplitude. It follows for the remaining energy after a time t fracEtE_ leftfracAtA_right^ leftfracA_-a tA_right^ ratioF left-atimestbright^ ratio approx resultratiopercP abcliste
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Exercise:
A damped oscillation hasprv a linear envelope with an initial amplitude AO and a decrease rate of aO. The oscillation frequency is fO. abcliste abc Graph the oscillation until the amplitude has dropped to zero. abc What fraction of the oscillation energy is left after tbO? abcliste

Solution:
abcliste abc The oscillation period is T TF fracf TP The linear envelope can be expressed as At A_ -a t with aaO. The amplitude has dropped to zero when -a t_ Longrightarrow t_ tzF fraca tzP These values result in the following graph: center includegraphicswidthtextwidth#image_path:linear-envelop# center abc The oscillaltion energy is proportional to the square of the amplitude. It follows for the remaining energy after a time t fracEtE_ leftfracAtA_right^ leftfracA_-a tA_right^ ratioF left-atimestbright^ ratio approx resultratiopercP abcliste
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Attributes & Decorations
Branches
Damped Oscillations
Tags
energy, envelope
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration