The same analysis is repeated using pure lagrange

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Unformatted text preview: /T = 60 Hz τ = RC 0 < t < T0: Vs(t) = Vsl*COS(.t) T0 < t < T01: Vs(t) = V0*EXP (-(t-T0)/τ) T01 < t < T: Vs(t) = Vsl*COS(ω.t) How to Find T0 and T01 For T0 we have: dVs( t ) dVs( t ) dt ( t < T0) = dt ( t > T0) V0 t − T0 Vs1cos(ωt ) exp( − )=− −ωVs1sin(ωt ) = − τ τ τ 1 1 t = arctan( ) ωτ ω Due to the discontinuity of the function, T01 must be found using a Newton's Method algorithm which can be done using ANSYS. The code that performs this operation can be found in the input listing. T01 verifies this equation: Vs1cos(ωt ) = Vo exp( − t − T0 τ ) Compute only the first three Fourier coefficients: a0, a1 and b1. First Fourier Coefficient: T ∫ 2 a0 = Vs( t ) dt T 0 a0 = Vs1 π (sin(ωT0) − sin(ωT01)) + 2 V 0τ T01 − T0 1 − exp − T τ Second Fourier Coefficient: 1–526 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. VM226 T ∫ 2 a1 = Vs( t )cos(ωt ) dt T 0 T0 T 2 2 2 a1 = Vs1 * cos (ωt ) dt + Vs1 * cos (ωt ) dt + A1 T To1 0 2Vs1 T0 + T − T01 1 a1 = + (sin(2ωT0) − sin(2ω...
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This note was uploaded on 12/09/2010 for the course DEPARTMENT E301 taught by Professor Kulasinghe during the Spring '09 term at University of Peradeniya.

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