 If it is assumed that the angle is much less than 1 radian (often cited as less than 0.1 radians, about 6°), or

then substituting for into using the small-angle approximation,

yields the equation for a harmonic oscillator,

The error due to the approximation is of order (from Taylor expansion for ).Given the initial conditions and , the solution becomes

The motion is simple harmonic motion where is the amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical).The period of the motion, the time for a complete oscillation (outward and return) is

which is known as Christiaan Huygens's law for the period.