# Math Help - critical gain

1. ## critical gain

Hi there;

How to calculate the critical gain needed for the output signal to begin to oscillate when a step (1) signal is used as the input and the transfer function of the main branch of a closed-loop system with negative unit feedback is known? Something like this:

For now, I just keep guessing and it looks like it's something between 3.5 and 3.6.

Help appreciated.

2. Originally Posted by disclaimer
Hi there;

How to calculate the critical gain needed for the output signal to begin to oscillate when a step (1) signal is used as the input and the transfer function of the main branch of a closed-loop system with negative unit feedback is known? Something like this:

For now, I just keep guessing and it looks like it's something between 3.5 and 3.6.

Help appreciated.
Try writing the ODE satisfied by the output (its a linear constant coefficient inhomogeneous ODE). To get ringing you need at least one complex root of the characteristic equation.

CB