Two children are playing on the swings in the friendly neighbourhood park. A claim is made by a student that the swing can be modeled by forced harmonic motion {i.e_ simple harmonic motion that is being pushed}. Using this model1 the horizontal position P of the swing relative to center of the swing structure is given by: P = Am] ~cos{o.rt) where t is time [in seconds], to is the frequency [in radians per second) at which the swing is pushed1 and the direction the children are Facing is the positive direction. Also, A is the amplitude [in meters] of the swing, as a function of w: 5 '4'\") = W In summary, at time t and with a pushing frequency of to. the horizontal distance of the swing from the centre line. is given by P = Au) oosot]. 1. Find E. At pushing frequency w = 1 is this derivative positive. negative. or zero, and what does this indicate physically? 2. Now suppose w is constant. dP s21:r [a] Find E and W. What do these derivatives represent? [LP 0121? 2:: . . . . [b] Evaluate E and F for t = T and m =1. Use your answers to determme whether the swing Is speeding up or slowing down, and in which direction