Solve #1,2 with work

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(w) . 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 A ( W ) - 3 3( 2 - W2 ) 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 . At pushing frequency w = 1 is this derivative positive, negative, or zero, and what does this indicate dw physically? 2. Now suppose w is constant. (a) Find ap and d' p dt dt2 . What do these derivatives represent? (b) Evaluate - dp and -P dt d42 for t = 3 and w = 1. Use your answers to determine whether the swing is speeding up or slowing down, and in which direction