In this formulation, we begin by writing Newton's second law, which gives the force \(F\) required to give an acceleration \(a\) to a mass \(m\) : Generally the force is a function of \(x\). Since the...In this formulation, we begin by writing Newton's second law, which gives the force \(F\) required to give an acceleration \(a\) to a mass \(m\) : Generally the force is a function of \(x\). Since the acceleration \(a=d^{2} x / d t^{2}\), Eq. \(\PageIndex{1}\) may be written This is a second-order ordinary differential equation, which we solve for \(x(t)\) to find the position \(x\) at any time \(t\). Solving a problem in Newtonian mechanics then consists of these steps:
