For simple harmonic vibrations y 1 = 8 c o s ω t y 2 = 4 c o s ⁡ ( ω t + π 2 ) y 3 = 2 c o s ⁡ ( ω t + π ) y 4 = cos ⁡ ω t + 3 π 2 are superimposed on one another. The resulting amplitude and phase are respectively

Step-by-step solution

Resultant displacement along X - axis is x = y 1 - y 3 = 8 - 2 = 6 Resultant displacement along Y - axis is y = y 2 - y 4 = 4 - 1 = 3 Net displacement, r = x 2 + y 2 = 6 2 + 3 2 = 45 Also, tan ⁡ θ = y x = 3 6 = 1 2