75. Add two harmonic oscillations of the same frequency and the same direction: x1 = A1cos (ωt + φ1) and x2 = A2cos (ωt + φ2). Draw a vector diagram for the time t = 0. Determine analytically the amplitude A and the initial phase φ of the resulting fluctuations. Postpone A and φ in the vector diagram. Find the equation of the resulting fluctuations (in the trigonometric form through the cosine). The problem solved for two cases: 1) A1 = 1 cm, φ1 = π / 3; A2 = 2 cm, φ2 = 5π / 6; 2) A1 = 1 cm, φ1 = 2π / 3; A2 = 1 cm, φ2 = 7π / 6.

Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)