The displacement of a particle as a function of time t is given by y(t) = ( t) + (2 t) . Which of the following statements correctly describes the nature of this motion and its fundamental time period?

Step-by-step solution

The given displacement function is a superposition of two trigonometric functions: y(t) = ( t) + (2 t) . Both individual terms represent periodic motions. The time period of the first term, ( t) , is T₁ = 2 . The time period of the second term, (2 t) , is T₂ = 2 2 = . For the superposition of two periodic functions to be periodic, the ratio of their time periods must be a rational number. Here, T₁ T₂ = 2 , which is rational. Thus, the combined motion is periodic. The fundamental time period of the combined motion i