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 = Au] - 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 \"\"3: W In su mmaryr at time t and with a pushing frequency of w, the horizontal distanoe of the swing from the centre line, is given by P = Aha) casket]. 1. Find At pushing frequency w = 1 is this derivative positive. negative, or zero. and what doa this indicate physica ly? 2_ Now suppose to is constant (a) Find % and % What do thae derivatives represent? (b) Evaluate E and for t = 2\" and w = 1. Use your answers to determine whether the swing is speeding dt cit? up or slowing down, and in which direction