From the equations given below select the correct equation representing the displacement of a particle undergoing a periodic motion. [ y - displacement; a - amplitude T - Period; - angular velocity; t -time]

Step-by-step solution

The general equation for the displacement of a particle undergoing simple harmonic motion is given by y = a ( t + ) , where is the angular frequency and t is the time. The relationship between angular frequency and the time period T is defined as = 2 T . Substituting this expression for into the general displacement equation, we get y = a ( 2 T t ) . Rearranging the terms inside the sine function, we obtain y = a ( 2 t T ) . Answer: y=a [ (2 t ) T ]