ODE's

• b^2-4ac=0?

  critically damped

  decays without oscillation
• b^2-4ac>0?

  overdamped

  decays without oscillation
• b^2-4ac<0?

  underdamped

  oscillates
• real and distinct, negative eigenvalues?

  overdamped

  decays without oscillation
• real and repeated, negative eigenvalue?

  critically damped

  decays without oscillation
• complex eigenvalues, negative real part?

  underdamped

  oscillation with decay
• purely imaginary eigenvalues?

  undamped

  oscillates with no decay