Physics - Phase Shift of Oscillators and Diffraction

Hi guys, I have two problems that have been bothering me for a while and I'm wondering if anybody can help explain it to me. Also, sorry in advance, I can't seem to make a new line via "return". When considering a driven oscillator at resonance, modelled by the equation mx'' = -kx + Fcos(wt). where k is the spring constant, Fcos(wt) is the driving force and w is the driving frequency - why must the solution to the differential x(t), be either exactly in phase or 180 degrees out of phase with the driving force, F(t)? As for diffraction, a similar issues comes up for me; for a double slit experiment, the formula is nL = 2dsin(t). Why must destructive interference arise when the two waves are a half cycle out of phase (or a multiple of)? My apologies again for the block of unformatted text.