Simple pendulum

Virtual simple-pendulum laboratory: drag the bob to set the initial angle and release it to start the damped oscillatory motion. Measurements are taken by a timer (Time mode) or a speedometer (Speed mode) as the bob crosses the reference line, with configurable artificial random and systematic measurement errors.

Drag the bob to set the initial angle, then release it to start the motion. On the meter, click the circles to select Time mode (which measures the time interval between the pendulum's first two crossings of the dashed reference line) or Speed mode (which measures the pendulum's speed as it crosses that line).

This simulation numerically solves the damped-pendulum ODE using the fourth-order Runge–Kutta method $$ \ddot{\theta} + \gamma\dot{\theta} + \dfrac{g}{L}\sin\theta = 0 $$ with gravitational acceleration $g = 9.8$ m/s$^2$ and damping factor $\gamma = 0.05$ s$^{-1}$.

The error $\alpha$ is generated by a random variable: each time the time interval or speed is calculated, a value $\alpha$ is drawn from the interval $[-\epsilon, \epsilon]$ and added to the value reported by the device. $\epsilon$ is the noise amplitude. The value of $\alpha$ has two components: random error (a Gaussian distribution centered on the calculated value) and systematic error (an offset added to the calculated value).

Marco P. M. de Souza