For example, a rigid uniform rod of length L {\displaystyle L} pivoted about one end has moment of inertia I = 1 3 m L 2 {\textstyle I={\frac {1}{3}}mL This article is about the weight suspended from a pivot. For other uses, see Pendulum (disambiguation). "Simple gravity pendulum" model assumes no friction or air resistance.

For real pendulums, the period varies slightly with factors such as the buoyancy and viscous resistance of the air, the mass of the string or rod, the size and shape of the bob and how it is attached to the string, and flexibility and stretching of the string. [11] [13] In precision applications, corrections for these factors may need to be applied to eq. (1) to give the period accurately. Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum. A compound pendulum has the same period as a simple gravity pendulum of length L eq {\displaystyle L_{\text{eq}}} , called the radius of oscillation, equal to the distance from the pivot to a point called the center of oscillation. [14] This point is located under the center of mass of the pendulum, at a distance which depends on the mass distribution of the pendulum. If most of the mass is concentrated in a relatively small bob compared to the pendulum length, the center of oscillation is close to the center of mass. [15] t ) = θ 0 cos ⁡ ( 2 π T t + φ ) {\displaystyle \theta (t)=\theta _{0}\cos \left({\frac {2\pi }{T}}\,t+\varphi \right)}

GIFs