*4. Find the Fourier series for sin t]. An oscillating system with natural frequency w (a constant) forced by a rectified sine wave satisfies the ODE ²y +w²y = | sint. dt² Find the particular solution y, for this ODE. For what values of w does resonance (i.e. the solution becomes unbounded) occur?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the Fourier series for |sin t|. An oscillating system with natural frequency ω (a constant) forced by a rectified sine wave satisfies the ODE d 2 y dt2 + ω 2 y = |sin t|. Find the particular solution yp for this ODE. For what values of ω does resonance (i.e. the solution becomes unbounded) occur? 

*4. Find the Fourier series for sin t|. An oscillating system with natural frequency w (a
constant) forced by a rectified sine wave satisfies the ODE
dy
dt²
+w²y = | sin t|.
Find the particular solution yp for this ODE. For what values of w does resonance
(i.e. the solution becomes unbounded) occur?
Transcribed Image Text:*4. Find the Fourier series for sin t|. An oscillating system with natural frequency w (a constant) forced by a rectified sine wave satisfies the ODE dy dt² +w²y = | sin t|. Find the particular solution yp for this ODE. For what values of w does resonance (i.e. the solution becomes unbounded) occur?
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