Oscillation-time

Jupyter notebooks on numerical experimentation of the oscillation time in a nonlinear pendulum We consider a nonlinear pendulum modeled by $$ \frac{d^2x}{dt^2} + 2,\alpha \frac{dx}{dt} + \beta, \frac{dx}{dt}, \left| \frac{dx}{dt} \right| + x, \left(1+\gamma,f(x)\right)=0, \qquad x(0) = x_0, \dot{x}(0) = 0. $$ Denote by $\tau(x_0, \alpha, \beta)$ the time taking by the pendulum to complete one oscillation starting at $x_0$ with vanishing velocity. Fixed $x_0$, this notebook explores the dependence of $\tau$ on the damping coefficients $\alpha$ and $\beta$. The effect of an additional parameter $\gamma$ is also considered