Exercise
https://texercises.com/exercise/linear-envelope/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
The amplitude of an oscillation with linear envelope decreases by percAO of the initial value within tAO. How long does it take the energy to decrease to percEO of its initial value?

Solution:
The amplitude decreases linearly: At A_left-k tright A_left-fracDelta AA_ fractDelta tright The energy is proportional to the square of the amplitude. It follows that fracEtE_ leftfracAtA_right^ left-fracDelta AA_ fractDelta tright^ We can solve this expression for the time t: -fracDelta AA_ fractDelta t sqrtfracEtE_ fracDelta AA_ fractDelta t -sqrtfracEtE_ t tEF tAtimesleft-sqrtfracpercEOperctotrightfracperctotpercAO tE approx resulttEP
Meta Information
\(\LaTeX\)-Code
Exercise:
The amplitude of an oscillation with linear envelope decreases by percAO of the initial value within tAO. How long does it take the energy to decrease to percEO of its initial value?

Solution:
The amplitude decreases linearly: At A_left-k tright A_left-fracDelta AA_ fractDelta tright The energy is proportional to the square of the amplitude. It follows that fracEtE_ leftfracAtA_right^ left-fracDelta AA_ fractDelta tright^ We can solve this expression for the time t: -fracDelta AA_ fractDelta t sqrtfracEtE_ fracDelta AA_ fractDelta t -sqrtfracEtE_ t tEF tAtimesleft-sqrtfracpercEOperctotrightfracperctotpercAO tE approx resulttEP
Contained in these collections:

Attributes & Decorations
Branches
Damped Oscillations
Tags
damping, energy, linear envelope
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link