Description
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.
Controls
Arraste a bolinha para definir o ângulo inicial; solte para iniciar o movimento. No medidor, clique nos círculos para escolher o modo Tempo (mede o período: o intervalo de tempo entre a 1ª e a 3ª passagem do pêndulo pela linha de referência tracejada, uma oscilação completa) ou Velocidade (mede a velocidade do pêndulo ao passar por essa linha).
Physical model
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$^{-1}$.
Measurement errors
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).
Developers
Marco P. M. de Souza
References
S. Thornton, J. Marion, Classical Dynamics of Particles and Systems (Cengage Learning, 2011).