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https://texercises.com/exercise/velocity-and-displacement/
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Exercise:
A mass oscillates on a spring with a period of TO and an amplitude AO. Calculate the displacement where the mass moves with a velocity of vO.

Solution:
The conservation of energy can be expressed as fracm sscvmax^ fracm v^ + frack y^ labeleq_coe We also know that sscvmax omega A labeleq_vmax and omega frackm labeleq_om Upon dividing refeq_coe by the m/ and using refeq_vmax and refeq_om we find sscvmax omega^ A^ v^+frackmy^ v^+omega^ y^ Solving for the displacement y yields y sqrtA^-fracv^omega^ sqrtA^-fracv^pi/omega^ yF sqrtA^-fracvtimes T^pi^ y approx resultyP-
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\(\LaTeX\)-Code
Exercise:
A mass oscillates on a spring with a period of TO and an amplitude AO. Calculate the displacement where the mass moves with a velocity of vO.

Solution:
The conservation of energy can be expressed as fracm sscvmax^ fracm v^ + frack y^ labeleq_coe We also know that sscvmax omega A labeleq_vmax and omega frackm labeleq_om Upon dividing refeq_coe by the m/ and using refeq_vmax and refeq_om we find sscvmax omega^ A^ v^+frackmy^ v^+omega^ y^ Solving for the displacement y yields y sqrtA^-fracv^omega^ sqrtA^-fracv^pi/omega^ yF sqrtA^-fracvtimes T^pi^ y approx resultyP-
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Branches
Harmonic Oscillations
Tags
angular frequency, conservation of energy, displacement, elastic energy, kinetic energy, period, velocity
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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