Share
Explore BrainMass

# Energy - An interesting one-dimensional system is the simple pendulum, consisting of a point mass m, fixed to the end of a massless rod (length l)

An interesting one-dimensional system is the simple pendulum, consisting of a point mass m, fixed to the end of a massless rod (length l), whose other end is pivoted from the ceiling to let it swing freely in a vertical plane, as shown in Figure 4.26. The pendulum's position can be specified by its angle &#963; from the equilibrium position. (It could equally be specified by its distance s from equilibrium-indeed s=l&#963;-but the angle is a little more convenient.) (a)Prove that the pendulum's potential energy (measured from the equilibrium level) is

U(&#963;)=mgL_little(l-cos&#963;)

Write down the total energy E as a function of &#963;_dot. (b) Show that by differentiation your expression for E with respect to t you can get the equation of motion for &#963; and that the equation of motion is just the familiar &#1168;=Ialpha (Where &#1168; is the torque, I is the moment of inertia, and alpha is the angular acceleration &#963;_double-dot). (c) Assuming that the angle &#963; remains small throughout the motion, solve for &#963;(t) and show that the motion is periodic with period
&#964;_0=2&#960;&#8730;(L_little/g)

I need help with this problem. Outline of solution please

#### Solution Summary

An interesting one-dimensional system is the simple pendulum, consisting of a point mass m, fixed to the end of a massless rod (length l).

\$2.19