
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 2,073 Thanks: 695 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.


Tags 
equation, friction, motion, pendulum, undamped 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
conservation of energy in an undamped driven harmonic oscillator  inkliing  Physics  2  August 26th, 2014 08:48 AM 
projectile motion, how to get the equation for range in projectile motion  sweer6  New Users  4  May 21st, 2014 11:00 PM 
Need help solving this friction equation!  Girn  Algebra  6  September 30th, 2012 10:27 PM 
Simple pendulum equation turned into a different form  chutsu  Applied Math  0  October 12th, 2010 03:50 AM 
Motion equation  Michael K  Calculus  1  December 17th, 2008 08:03 AM 