Equation of Motion

The force on an object having mass $m$ and acceleration $a$ may be determined using Newton's second law of motion

$$F = ma.$$

There is an elastic force restoring the mass to its equilibrium position, given by Hooke's law

$$F = -Kx,$$

where $K$ is a constant describing the stiffness of the spring.

The spring force is equal and opposite to the force due to acceleration, yielding the equation of motion:

$$m\frac{d^2x}{dt^2} = -Kx.$$