1-DOF Duffing time response

The time-response quickstart is the canonical runnable example. A time response is the right diagnostic before a frequency sweep: it lets you inspect whether the transient estimate, sampling, and response regime make sense for your parameter set.

Use only_save_steady_state=False while validating a new model. Plot response.displacement and response.velocity to inspect settling and create a phase portrait. Once the transient is credible, setting only_save_steady_state=True reduces returned data to the final retained window.

response = solver.time_response(
    x0=jnp.array([0.0]),
    v0=jnp.array([0.0]),
    only_save_steady_state=False,
)

The solver estimates the transient from a linear model. Strong nonlinearities can require a larger t_steady_state_factor; see accuracy, performance, and limitations.