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 = 0.0125 .

Step-by-step solution

The total displacement of the particle is given by the principle of superposition: x = x₁ + x₂ Substituting t = 0.0125 into the equation for x₁ : x₁ = 2.0 (100 0.0125) x₁ = 2.0 (1.25 ) = 2.0 ( 5 4 ) x₁ = 2.0 (- 1 2 ) = - 2 -1.414 cm Substituting t = 0.0125 into the equation for x₂ : x₂ = 2.0 (120 0.0125 + 3 ) x₂ = 2.0 (1.5 + 3 ) = 2.0 ( 3 2 + 3 ) Using the trigonometric identity ( 3 2 + ) = - : x₂ = -2.0 ( 3 ) = -2.0 1 2 = -1.0 cm The total displacement at t = 0.0125 is: x = x₁ + x₂ = -1.414 - 1.0 = -2.414 cm Round