Question

mg mg sin Here it is assumed that the mass is released with zero velocity at an initial angle, 0 < α < π. We would like to determine the equation of motion for the pendulum and its period of oscillation. Do the following. The period P of the pendulum is defined to be the time required for it to swing from one extreme to the other and back-that is, from α to-α and back to α. Show that the period is given by 4.1 аф The integral in (6) is called an elliptic integral of the first kind and is denoted by F(k,"). As you might expect, the period of the simple pendulum depends on the length 2 l of the rod and the initial displacement a. In fact, a check of an elliptical integral table will show that the period nearly doubles as the initial displacement increases from 15π to 8 (for fixed l), what happens as aapproaches π? 16

Answer 1

te 仃 2.3 00