Computer Measurement of a Spring Pendulum in a Vertical Plane by Using the Two-Dimensional Position Sensitive Detector

受光平面上の光点位置を，2次元で検出できる半導体素子を応用して，ばね振子の鉛直面内運動をコンピュータ計測した。光点位置検出素子は，平面状シリコンの表面にP層，裏面にN層，中間にI層の構造を持ち，受光面に光スポットが入射すると，入射位置には光エネルギーに比例した電荷が発生し，電荷は光電流としてP層を通過，電極までの距離に逆比例して分割され，光点位置を知る情報を電極に出力する。浜松ホトニクス製の素子S1880の有効受光面は12mm×12mmであり，一眼レフカメラの本来のフィルム位置に装着し，測定物体に取り付けた発光ダイオードからの光がレンズ系を通して受光面に投射される。信号処理回路を経て，受光面中央を基準としたX座標とY座標が，1V/mmの割合で電圧に変換され，コンピュータで1秒間に250回の速さで運動体の座標を計測取得する。各種の平面運動の非接触測定に応用できるが，今回は，ばね振子の鉛直面内運動に適用した。錘は複雑な運動を行うが，左右に1回振動する間に，上下に2回振動するように，条件を整えると，振子は左右振動と上下振動との間で，顕著にエネルギーを交換する。錘の質量を変えて実験を行い，シミュレーションとも良い一致を得た。物理教育実験の開発例として報告する。The motion of a spring pendulum in a vertical plane was executed by computer measurement applying the semiconductor device that is able to detect the position of a light spot on the plane with two dimensions. The position sensitive detector has the structure of the P layer on the surface, the N layer on the back surface and the intermediate I layer of plane silicone. When a light spot enters on the receiving surface, the electric charge proportional to light energy generates on the incident position. The electric charge flows through the P layer as a light current and is divided proportional to the inverse of the distance to the electrodes in order to give the information of the light spot position. The effective light receiving surface of the element S1880 made of Hamamatsu Photonics is 12mm by 12mm and the position sensitive detector is located to the original position of film of a reflex camera. The light from an emitting diode mounted to the measured object is projected to the receiving surface through the lens system. X coordinates and Y coordinates on the basis of the surface center are transformed to the voltage with 1V/mm through the signal processing circuit and the coordinates of the object are measured at the speed of 250 times a second with a computer. Although this optical method can be applied to non-contact measurement of various plane motions, this time it applied to the motion of a spring pendulum in a vertical. The weight of pendulum moves complicatedly. When a condition is arranged as it oscillates twice up and down while it oscillates once right and left, the pendulum exchanges energy conspicuously between the horizontal oscillation and the vertical oscillation. The experiment was carried out changing mass of the weight and the experimental results are compared with simulations. This is reported as an example of the development of the physics education experiment