 Some examples of Newton's law include describing the motion of a simple pendulum,

and a damped, sinusoidally driven harmonic oscillator,

For describing the motion of masses due to gravity, Newton's law of gravity can be combined with Newton's second law.For two examples, a ball of mass thrown in the air, in air currents (such as wind) described by a vector field of resistive forces ,

where is the gravitational constant, the mass of the Earth, and is the acceleration of the projectile due to the air currents at position and time .The classical -body problem for particles each interacting with each other due to gravity is a set of nonlinear coupled second order ODEs,

where labels the quantities (mass, position, etc.)