Practice question · Multiple choice
The damped oscillator’s behaviour changes qualitatively as damping increases, passing through a critical value. Why does the behaviour change qualitatively at that value?
Hints
- Look at the discriminant of the characteristic equation.
- Complex roots give oscillation; real roots do not.
Show the answer
D. The characteristic roots become real, so oscillation stops
Why
The discriminant changes sign and complex roots become real. This is why critical damping is the design target for a door closer or a car suspension: fastest return with no overshoot.
Practise Second-Order Linear ODEs
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