First of all, according to the simple harmonic vibration, the force is inversely proportional to the displacement, that is, F=-kx and k is the coefficient. Then according to Newton's second law F=ma, we know that a=-(k/m)x, because A = (d 2) x/dt 2, we get

(D2)x/dt ^ 2+(k/m)x = 0。 Solve this differential equation to get the displacement x, then take the derivative of x to get the velocity v, and finally take the derivative of v to get a.

If a is known, the velocity v can be obtained by integrating a, and then the displacement x can be obtained by integrating v.