Problem 8 Show that the solution given for an underdamped harmonic oscillator, x(t) = Ae-bt/2m$), is a solution to the following differential equationcos(w't+b dxk= 0.-r ==dt2т dtmk62Where w' =m4m2

Name: Problem 8 Show that the solution given for an underdamped harmonic os
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Description: Problem 8 Show that the solution given for an underdamped harmonic oscillator, x(t) = Ae-bt/2m$), is a solution to the following differential equationcos(w't+b dxk= 0.-r ==dt2т dtmk62Where w' =m4m2

Given, xt=Ae-bt2mcosω't+ϕnow, dxdt= -b2mAe-bt2mcosω't+ϕ-Aω'e-bt2msinω't+ϕ…

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Problem 8 Show that the solution given for an underdamped harmonic oscillator, x(t) = Ae-bt/2m cos(w't+ $), is a solution to the following differential equation d?x b da k dt2 + -x = (0. т dt т Where w' k h2 4m2 · m

Problem 8 Show that the solution given for an underdamped harmonic oscillator, x(t) = Ae-bt/2m cos(w't+ $), is a solution to the following differential equation d?x b da k dt2 + -x = (0. т dt т Where w' k h2 4m2 · m

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 15CQ: Give an example of a damped harmonic oscillator. (They are more common than undamped or simple...

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