External Excitation Characteristics and Computer Measurement of a Gradually Hard Pendulum

鉛直に張ったばねを，ばねに対して横に引くと，変位に比例しない非線型復元力が得られ，ばねを緩く張るときは，振幅の増加と共に周期が減少する漸硬ばねに，強く張るときは，振幅の増加と共に周期が増加する漸軟ばねになる。既に種々報告してきた物理振子の復元力は漸軟ばねに対応し，その外部励振特性と比較検討するために，試作の漸硬振子に，一定振幅の正弦回転力を印加し，周期を徐々に自動掃引して，一連のデータをコンピュータで測定した。非線型振動特有の振幅飛躍現象と履歴現象が得られ，骨格曲線の特性が異なるため，物理振子とは逆の性質を示した。運動方程式を数値的に解き，シミュレーションと実験結果との比較を行った。漸硬と漸軟を対比して，非線型，並びに，線型強制振動について論じた。An experiment about the nonlinear forced oscillation of a pendulum whose period decreases with increasing amplitude is investigated with a computer.The nonlinear force of restoration to the pendulum is given by transverse displacement of a spring stretched vertically.The system is driven by an externally applied sinusoidal force in order to compare with the physical pendulum previously reported.The experiment clearly revealed two distinct nonlinear phenomena-one a phenomenon of discontinuous jumps in the amplitude of oscillation as a function of the period of the driving force,the other a phenomenon of hysteresis loop in the amplitude-period curve:when the period of external force is increased and when the same is decreased the discontinuous jumps in the amplitude take place at different periods of the external force.Excitation characteristics are completely contrary to the physical pendulum,as the skeletal curve has the reverse property.The motions of the pendulum are also numerically analysed by means of computer simulations and the experimental results are compared with the simulations