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0/10/2/4/5 . Beispiel 11 - 64
Stellen Sie die Harmonischen Schwingungeny1 = 3 ⋅ cos(ωt -π 4 ) und y2 = -3 ⋅ sin(ωt -π 6 ) durch eine Sinusfunktion vom Typ y = A ⋅ sin(ωt + ϕ) dar. .
y1 = 3 ⋅ cos(ωt -π 4 ) = 3 ⋅ sin(ωt + π 4 ) . y2 = -3 ⋅ sin(ωt -π 6 ) = 3 ⋅ sin(ωt + 5π 6 ) .
y = A ⋅ sin(ωt + ϕ) . und A1 = A2 = 3, φ1 = π 4 , φ2 = 5π 6 mit A = A1 2 + A2 2 + A1 A2 cos (φ1 - φ2 ) = 9 + 9 + 9 ⋅ cos ((1 4 -1 6)π) = 18 + 9 ⋅ cos (( 3 12 - 2 12)π) = 18 + 9 ⋅ cos ( 1 12π) ≈18 + 9 ⋅ 0, 991 ≈26, 9 ≈ 5, 188. . tan φ = y1 + y2 x1 + x2 = A1 ⋅ sin φ1 + A2 ⋅ sin φ2 A1 ⋅ cos φ1 + A2 ⋅ cos φ2 = sin π 4 + sin 5π 6 cos π 4 + cos 5π 6 ≈-7.595 . φ ≈ arctan -7.595 ≈-1, 44 ≈ 82°. .