Exercise
https://texercises.com/exercise/half-speed/
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:
For a mass on a spring determine the displacement as a fraction of the amplitude for which the velocity is half the maximum velocity.

Solution:
The total energy can be expressed as the maximum elastic energy left or the kinetic and elastic energy at the displacment where the kinetic energy corresponds to half the maximum velocity: frack A^ frack y^+fracm v_y^ frack y^+fracm leftfracsscvmaxright^ The second term on the right can be written as fracm leftfracsscvmaxright^ fracsscEkinmaxfracsscEelmaxfracfrack A^ It follows that frack y^frack A^- fracfrack A^ fracfrack A^ Longrightarrow y resultfracsqrtA
Meta Information
\(\LaTeX\)-Code
Exercise:
For a mass on a spring determine the displacement as a fraction of the amplitude for which the velocity is half the maximum velocity.

Solution:
The total energy can be expressed as the maximum elastic energy left or the kinetic and elastic energy at the displacment where the kinetic energy corresponds to half the maximum velocity: frack A^ frack y^+fracm v_y^ frack y^+fracm leftfracsscvmaxright^ The second term on the right can be written as fracm leftfracsscvmaxright^ fracsscEkinmaxfracsscEelmaxfracfrack A^ It follows that frack y^frack A^- fracfrack A^ fracfrack A^ Longrightarrow y resultfracsqrtA
Contained in these collections:

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