Motion of a pendulum

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  • The nonlinear vibration of a pendulum whose support undergoes arbitrary rectilinear harmonic motion is studied. The main attention is paid to the resonant cases and the stationary vibrations. The resonant conditions are explained. The amplitude - frequency curves are plotted for various values of parameters and the stability of vibration is investigated. The rotating motion of the pendulum and its stability are also considered.

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  • The purpose of this lab is to explore the dynamics of the simple harmonic oscillator (SHO). To make things a bit more interesting, we will model and study the motion of an inverted pendulum (IP), which is a special type of tunable mechanical oscillator. As we will see below, the inverted pendulum contains two restoring forces, one positive and one negative.

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  • It is shown that this approach makes it possible to reduce considerably the number of unknowns of the problem and reduce it description only to parameters of motion of a liquid free surface and parameters of motion of a carrying body. The constructed nonlinear discrete model of the system was applied for investigation of motion of a reservoir with liquid on pendulum suspension, on taking into account liquid outflow and other problems, which have theoretical and applied meaning.

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