Student-Friendly Precision Pendulum Germany (latitude 52 N → 981,274) in the early part of this century. With the information provided in this article, students should be able to easily measure the gravitational field strength to a few parts in 10,000, a degree of precision one to two orders of magnitude better than can be achieved with the usual simple pendulum under comparable conditions. The...

Abstract In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For first time, a new and exact expression is obtained for the time “t” of swinging of a simple pendulum from the vertical position to an arbitrary angular position “θ”. The time period “T” of such a pendulum is also exactly expressible in terms of hypergeometric functions.

We consider the simple pendulum equation −u′′(t) + f(u′(t)) = λ sinu(t), t ∈ I := (−1, 1), u(t) > 0, t ∈ I, u(±1) = 0, where 0 < ≤ 1, λ > 0, and the friction term is either f(y) = ±|y| or f(y) = −y. Note that when f(y) = −y and = 1, we have well known original damped simple pendulum equation. To understand the dependance of solutions, to the damped simple pendulum equation with λ 1, upon the te...

The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism and the set up of three simple experiments are presented in order to probe our approach.

The theory behind small amplitude movement of a single pendulum is stated, followed by the construction of a simple example of a coupled pendulum with two degrees of freedom including the unidirectional movement of the structure and the pendulum angle in relation to vertical. These models and the finite elements software SAP 2000 are also applied to a single and to a multiple degree of freedom ...

The inverted pendulum is a simple system in which both stable and unstable configurations are easily observed. The upward inverted state is unstable, though it has long been known that a simple rigid pendulum can be stabilized against small disturbances in its inverted state by oscillating its pivot in an up-and-down motion. Numerical simulations of the inverted pendulum are employed to investi...