Solve y" + y = 1 12/1 if 0S t= T and 0 if to; here, y(0) = 0, y' (0) = 0. This models an undamped system on which a force F acts during some interval of time (see Fig. 59), for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At T both y and y' must be continuous. m = 1 k = 1 F F = 1- t2/T2 1 F = 0 t