A particle undergoes two simple harmonic motions described by x₁ = 2.0 100 t and x₂ = 2.0 (120 t + /3) , with x in centimeter and t in second. Determine the displacement of the particle at t = 0.025 .

Step-by-step solution

The total displacement of the particle is given by the principle of superposition: x = x₁ + x₂ Substituting t = 0.025 s into the equations for x₁ and x₂ : x₁ = 2.0 (100 0.025) = 2.0 (2.5 ) x₁ = 2.0 (2 + 2 ) = 2.0 ( 2 ) = 2.0 1 = 2.0 cm x₂ = 2.0 (120 0.025 + 3 ) = 2.0 (3 + 3 ) x₂ = 2.0 (- 3 ) = -2.0 3 2 = - 3 -1.732 cm The net displacement at t = 0.025 s is: x = 2.0 - 1.732 = 0.268 cm 0.27 cm