What will be the displacement equation of the simple harmonic motion obtained by combining the motions? x 1 = 2 sin ⁡ ω t , x 2 = 4 sin ⁡ ω t + π 6 a n d x 3 = 6 sin ⁡ ω t + π 3

Step-by-step solution

The resultant equation is x = A sin ⁡ ω t + ϕ ∑ A x = 2 + 4 cos ⁡ 30 ° + 6 cos ⁡ 60 ° = 8.46 And ∑ A y = 4 sin ⁡ 30 ° + 6 cos ⁡ 30 ° = 7.2 ∴       A = ∑ A x 2 + ∑ A y 2 =     8.46 2 + 7.2 2 = 11.25 And tan ⁡ ϕ = ∑ A y ∑ A x = 7.2 8.46 = 0.85 ⇒     ϕ = tan - 1 ⁡ 0.85 = 40.4 ° Thus, the displacement equation of combined motion is x = 11.25 sin &#8289