Consider a particle moving in uniform circular motion in the xy plane at a distance r=1.3 m from the origin. Refer to the figure. In this problem, you will show that the projection of the particle’s motion onto the x− axis can be used to represent simple harmonic motion. Part (a) If the particle moves counterclockwise at a constant angular velocity of ω , and at time t=0 its coordinates are (x,y)=(r,0) , enter an expression for the projection of the particle's position onto the x− axis, in terms of r , ω , and t . Part (b) For an angular speed of ω=6.8 rad/s , find the value of x , in meters, at time t=0.14 s . Part (c) Considering the expression you entered in part (a) for the projection of the particle’s position onto the x− axis, can the projection's motion be described as simple harmonic motion? Part (d) Which of the graphs correctly shows the projection of the position of the moving particle onto the x− axis as a function of t for two full cycles? Part (e) Enter an expression for the velocity function, vx , associated with the position function you entered in part (a), in terms of r , ω , and t . Part (f) For an angular speed of ω=6.8 rad/s , find the value of vx , in meters per second, at time t=0.14 s . Part (g) How is the velocity you entered in part (e) related to the tangential velocity of the particle undergoing uniform circular motion in the problem statement? Part (h) Enter an expression for the acceleration function, ax , associated with the position function you entered in part (a), in terms of r , ω , and t . Part (i) For an angular speed of ω=6.8 rad/s , find the value of ax , in meters per second squared, at time t=0.14 s . Part (j) In simple harmonic motion, the acceleration, ax , is directly proportional to the displacement, x , with a negative proportionality factor. Considering the expressions you entered in parts (a) and (h), is that true?