mass m is fixed to Pendulum A simple pendulum consisting of a point 1. the end of a massless rod (length /), whose other end is pivoted from the ceiling to let it swing freely in a vertical plane, specified by its angle o from the equilibrium position. (a) Prove that the pendulum's potential energy (measured from the equilibrium level) is as shown below. The pendulum's position can be U ()mgl (1 - cos ) (b) Write down the total energy E as a function of and o. Show that by differentiating your expression for E with respect to t you can get the equation of motion for ¢ and that the equation of motion is just the familiar T moment of inertia, and a is the angular acceleration ). (c) Assuming that the angle remains small throughout the motion, show that the motion is periodic with period Ia (where T is the torque, I is the - 2т V1/9. Tо m 1

mass m is fixed to Pendulum A simple pendulum consisting of a point 1. the end of a massless rod (length /), whose other end is pivoted from the ceiling to let it swing freely in a vertical plane, specified by its angle o from the equilibrium position. (a) Prove that the pendulum's potential energy (measured from the equilibrium level) is as shown below. The pendulum's position can be U ()mgl (1 - cos ) (b) Write down the total energy E as a function of and o. Show that by differentiating your expression for E with respect to t you can get the equation of motion for ¢ and that the equation of motion is just the familiar T moment of inertia, and a is the angular acceleration ). (c) Assuming that the angle remains small throughout the motion, show that the motion is periodic with period Ia (where T is the torque, I is the - 2т V1/9. Tо m 1

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

mass m is fixed to
Pendulum A simple pendulum consisting of a point
1.
the end of a massless rod (length /), whose other end is pivoted from the ceiling to let
it swing freely in a vertical plane,
specified by its angle o from the equilibrium position.
(a) Prove that the pendulum's potential energy (measured from the equilibrium level) is
as shown below. The pendulum's position can be
U ()mgl (1 - cos )
(b) Write down the total energy E as a function of and o. Show that by differentiating
your expression for E with respect to t you can get the equation of motion for ¢ and
that the equation of motion is just the familiar T
moment of inertia, and a is the angular acceleration ).
(c) Assuming that the angle remains small throughout the motion, show that the motion
is periodic with period
Ia (where T is the torque, I is the
- 2т V1/9.
Tо
m
1

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