In the rectangle ABCD, AB=4, BC=3, point P starts from point A and moves along the dotted line AD-DO-OC to the end point C at the speed of/kloc-0 per unit length per second. When point P does not coincide with point A, the intersection point P is PQ perpendicular to point Q, with PQ as the edge, square PQMN is made to the right, and the overlapping area of square PQMN and triangle ABD is S.
(2) Write directly the value range of t when the point O is in the square PQMN;
(3) When the point P moves on the broken line AD-DO, find the functional relationship between S and T;
(4) Write the value of t directly when the straight line DN bisects the area of the triangle BCD.