(1). Use Fourier Transforms to find the complete solution x(t) for the displacement of the damped, driven harmonic oscillator for the case of critical damping a² = wo². As described in class, x(t) satisfies: d²x(t) dt² dx(t) dt 2 + 2α +w₁²x(t) = A(t) and we will take the driving term A(t) to be given by A(t) = [Alt≤T 0,lt > T Note: as in the underdamped case (a² < w¸²) that was solved in class, you will 0 need to separately consider three cases († < −t,-t≤t≤t,t

(1). Use Fourier Transforms to find the complete solution x(t) for the displacement of the damped, driven harmonic oscillator for the case of critical damping a² = wo². As described in class, x(t) satisfies: d²x(t) dt² dx(t) dt 2 + 2α +w₁²x(t) = A(t) and we will take the driving term A(t) to be given by A(t) = [Alt≤T 0,lt > T Note: as in the underdamped case (a² < w¸²) that was solved in class, you will 0 need to separately consider three cases († < −t,-t≤t≤t,t

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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