The Physical Pendulum
.A real pendulum, usually called a physical pendulum, can have a complican distribution of mass, much different from that of a simple pendulum. Does a physic pendulum also undergo SHM If sowhat is its period shows an arbil!’VY physical pendulum displaced to one side I angle 8. The gravitational force 1,acts at its center of mass C, at a distance h from the pivot point O. In spite of their shapes, comparison of reveals only one important difference between an arbitrary physical pendulum at a simple pendulum. For a physical pendulum the restoring component F, sin 8 the gravitational force has a moment arm of distance h about the pivot point, rath than of string length L. In all other respects, an analysis of the physical pendulu weuld duplicate our analysis of the simple pendulum up throughAgai (for small 8m) we would 6nd that the motion is approximately SHM. If we replace L with h in we can write the period of a physic pendulum as,
physical pendulum. small amplitude). As with the simple pendulum, 1is the rotational inertia of the pendulum about However, now 1 is not simply (it depends on the shape of the physical pendulum but it is still proportional to m. A physical pendulum will not swing if it pivots at its center of mass. For mall this corresponds to putting h = 0 in That then predicts T – I which implies that such a pendulum will never complete one swing. Corresponding to any physical pendulum that oscillates about a given pivot pol o with period T is a simple pendulum of length Lo with the same period T. We CI find Lo with The point along the physical pendulum at distance Lo from point 0 is called the center of oscillation of the physical pendulum for the given suspension point.
A physical pendUlum. The restoring torque is hE sin 8. When II = O. center of mass C hangs directly below pivot PIlint O.