Solve y + y = 1 - t 2 / 2 ? if 0 < t < and 0 if t ?? ??; here,

Solve y" + y = 1 - t²/π^2?if 0tπ and 0 if t ?? ??; 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).

m = 1 k = 1 F F =1-t/n2 1 F=0 Fig. 59. Problem 24