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 model, the horizontal position P of the swing relative to center of the swing strUCture is given by: P = A(m) -cos(wt) where t is time (in seConds). w is the frequency (in radians per second) at which the swing is pushed, 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 Aha!) = m In summary, at time t and with a pushing frequency of w, the horizontal distance of the swing from the centre line, is given by P = A(w) cos[wt). 1. Find E' At Pushing frequency w = 1 is this derivative positive, negative, or zero, and what does this indicate physically? 2. Now suppose to is constant. (LP ({2}) [a] Find Tilt and dt2 . What do these derivatives represent? dP (PP 21,, _ _ _ _ (b) Evaluate E and E for t = F and w = 1. Use your answers to determine whether the svvlng Is speeding up or slowing down, and in which direction