My Math Forum The equation of motion of an undamped pendulum (i.e., there is no friction) is

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 November 16th, 2016, 08:09 AM #1 Newbie   Joined: Nov 2016 From: Isenguard Posts: 6 Thanks: 0 The equation of motion of an undamped pendulum (i.e., there is no friction) is mLy''-mgsin(y) The pendulum is made by attaching a weight of mass m to a very light and rigid rod of length L mounted on a pivot so that the system can swing in a vertical plane. Here y denotes the angle that the pendulum makes with the vertical (equilibrium) position and g is the acceleration of gravity. Note that −π/2 < y < π/2. The restoring force, due to gravity, is fre(y) = −mg sin y A) find the potential energy p(y) B) Find the mechanical energy E(t) So far all I have done is solved for y'' and got y''=(-g/L)sin(y), I have no idea where to begin to begin finding the potential or mechanical energy of the pendulum.
 November 16th, 2016, 09:14 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,132 Thanks: 717 Math Focus: Physics, mathematical modelling, numerical and computational solutions The general problem cannot be solved analytically for x(t) or v(t), which is why the question is asking for energy rather than x(t) or v(t). To answer the questions, find out what the formulae for potential energy and kinetic energy are and try to substitute those into the ODE you have before solving. Thanks from topsquark and Yeep

 Tags equation, friction, motion, pendulum, undamped

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post inkliing Physics 2 August 26th, 2014 08:48 AM sweer6 New Users 4 May 21st, 2014 11:00 PM Girn Algebra 6 September 30th, 2012 10:27 PM chutsu Applied Math 0 October 12th, 2010 03:50 AM Michael K Calculus 1 December 17th, 2008 08:03 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top