One reason that the harmonic oscillator is a conceptually important example is that it is good approximation for many systems near a stable mechanical equilibrium. For example, a pendulum has a stable equilibrium in the vertical position: if motionless there, it will remain there, and if pushed slightly, it will swing back and forth. Neglecting air resistance and friction in the pivot, the force upon the pendulum is gravity, and Newton's second law becomes d 2 θ θ d t 2 = − − g L sin ⁡ ⁡ θ θ , where L is the length of the pendulum and θ θ is its angle from the vertical. When the angle θ θ is small, the sine of θ θ is nearly equal to θ θ (see Taylor series), and so this expression simplifies to the equation for a simple harmonic oscillator with frequency ω ω = g / L .