nice video, but the statement "Critical damping provides the quickest approach to zero amplitude" is misleading. All the solutions of this model (underdamped, critically damped, overdamped) asymptotically approach to zero amplitude and none of them reach it exactly. The critical solution in the limit of infinite time goes fastest towards the zero amplitude (but even that may depend on the initial conditions), and for any practical purpose (for finite time and some measurement resolution), a specific underdamped solution can be found that will reach the equilibrium state faster than critical and all other solutions, with the exception for one type of initial conditions for which the specific overdamped solution reaches zero amplitude the fastest in both practical and asymptotic sens....
underrated IB clutch goat
nice video, but the statement "Critical damping provides the quickest approach to zero amplitude" is misleading. All the solutions of this model (underdamped, critically damped, overdamped) asymptotically approach to zero amplitude and none of them reach it exactly. The critical solution in the limit of infinite time goes fastest towards the zero amplitude (but even that may depend on the initial conditions), and for any practical purpose (for finite time and some measurement resolution), a specific underdamped solution can be found that will reach the equilibrium state faster than critical and all other solutions, with the exception for one type of initial conditions for which the specific overdamped solution reaches zero amplitude the fastest in both practical and asymptotic sens....