Mathematically, in SHM,why is x'' (acceleration) always in the direction if x increasing? So if he have a simple setup, an elastic spring on a smooth horizontal table, one end attached to a fixed point, the other to a particle. Let's say the fixed point is at the left end of the spring. If we take right as positive and we pull the particle to the right, stretching the spring, the tension acts to the left and hence the acceleration must be acting in the same direction, from Newton's 2nd law, OPPOSITE to the direction of x increasing since that's to the right. But my book and other resources I found say "acceleration is always in the direction of x increasing." So what does that mean? I mean if I just see the shm equation it does make sense that acceleration/force has a different sign to the displacement and acts to restore the particle to equilibrium and if we look at the graphs, acc graph is 180 degrees out of phase to the displacement graph so surely this means they always act in opposite direction? Why does my book keep insisting acc is always in the direction of positive x (that's what x increasing means, right?). I'm rally getting frustrated and any help is hugely appreciated.