The linear oscillator

Let us begin with this problem which is simple, to learn the basics about numerical solution of differential equations. In later chapters more complicated problems will be studied. In this case, p=2, and the potential is given by:

and the force is then:

The solution of Newton's differential equation

is the familiar simple harmonic motion

A noteworthy feature of these harmonic oscillations is that the angular frequency and the period T in (24) are independent of the amplitude A; both large and small oscillations have the same frequency .