Hi, is there anyone who help me about this question?


question ) if a control system has a transfer function as K/s^3+2s^2+4s+K , what must be the value of "K" to get a constant amplitude of sinusoidal sign from systems output?

 

If my memory serves me right, you need your system to be in the verge of instability, oscillating indefinitely. For that, you need the root of the denominator to be on the imaginary axis, that is, for any s=jω,
\(s^3+2s^2+4s+K=0\)

Take a second opinion on that, as I don't have time to revise it right now.