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Standard 2nd Order ODEs Natural Frequency and Damping Ratio
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=eJMf9CYHr6c
In this video we discuss writing 2nd order ODEs in standard form • xdd(t)+2*zeta*wn*xd(t)+wn^2*x(t) • where zeta = damping ratio • wn = natural frequency • We will see that the damping ratio and natural frequency characterize the behavior of the system • • Topics and timestamps: • 0:00 – Introduction • 4:05 – Definition of standard 2nd order form • 19:11 – Overdamped system (zeta greater than 1) • 25:58 – Critically damped system (zeta = 1) • 29:00 – Underdamped system (zeta less than 1) • 1:04:09 – zeta and wn relationship to pole locations • 1:12:32 – Example: Pendulum • Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/... • All Ordinary Differential Equation videos in a single playlist ( • Ordinary Differential Equations ) • #ODEs #OrdinaryDifferentialEquations • You can support this channel via Patreon at / christopherwlum or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!
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