Simple pendulum (planar) 2005-08-30 Dynamic simulation of a planar pendulum Laboratorio de Ingeniería Mecánica Manuel González Castro Manuel González Castro González Castro Manuel J. Lolo Universidad de La Coruña Laboratorio de Ingeniería Mecánica Escuela Politécnica Superior lolo@cdf.udc.es +34 981337400 Mendizabal s/n Ferrol 15403 Spain

The planar simple pendulum is composed by a lumped mass of 1 kg and a massless link of 1 m length. The system is under gravity effects (9.81 N/kg acting in the negative y direction). The position of the global reference frame is shown in the figure.

Planar simple pendulum

The analysis to be performed is a dynamic simulation with a duration of 2000 s. Initially, the system is at rest (all velocities are zero) and in horizontal position: the value for the x-coordinate of point P1 is +1.0 m.

The reference solution for this problem is the time-history of the position of point P1 (x and y coordinates). The maximun allowed errors are 1.0E-1 (low precission) and 1.0E-3 (high precission), measured with 4000 output steps and a threshold value of 1.0E-3.

The following information is provided:

  1. Time-history of the position of point P1, as text data file: A01_solution_data.txt
  2. Animation of the system, as AVI movie: (first 5 s) A01_solution_movie.avi
  3. Time-history of the position of point P1, as plot (first 10 s):

    Time-history of the coordinates of point P1

 CPU-time spent by the software to solve the problem (in s).