This paper gives a detailed analysis of the physics of simple pendulum and the equations governing the motion and velocity. The pendulum works in three modes: simple, damped and driving and driving only. The signatures are evaluated and simulated by the means of four different approaches: Euler method, Euler-Cromer method, 2 nd order Runge-kutta method and built-in ODE-23 matlab solver. The sim...

Simple and bifilar pendulum were used to measure the mass moments of inertia of three tennis rackets. The pendulum setups were filmed using an off-the-shelf camcorder, with a stopwatch in view to provide timing data. The measurement accuracy was assessed using calibration rods of known mass moment of inertia. The simple pendulum method was found to be most accurate (<1.0 % difference to theoret...

The phenomenon of dynamic stabilization of the inverted pendulum whose pivot is forced to oscillate with a high frequency in vertical direction is revisited. A simple physically meaningful explanation of the phenomenon is presented, followed by the derivation of an approximate quantitative criterion of stability. A computer program simulating the physical system is developed, which aids the ana...

We determined the Newtonian constant of gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672 34±0.000 14)×10(-11)  m3  kg(-1)  s(-2). This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value...

In this note we will derive the equations of motion for a compound pendulum being driven by external motion at the center of rotation. A compound pendulum is a pendulum consisting of a single rigid body rotating around a fixed axis. In contrast to the simple pendulum we studied in class, a compound pendulum can have an arbitrary distribution of mass, which means that it better models real-world...

This paper describes a new inverted pendulum system that is useful to illustrate important aspects of nonlinear control systems theory. The stabilization of the pendulum is to be achieved by the on–off action of two electromagnets; therefore, an adequate switching policy has to be applied. The pendulum can be controlled by a computer, using simple electronic interface circuits. This paper consi...

Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.