# Finding $\small K$ for a given $\small\zeta$ value when $\omega_n$ (frequency) is not given

Here $$\\omega_n\$$ (frequency) is not given.

Then upon plotting the Root Locus, how will we find $$\\small K\$$ at $$\\small\zeta = 0.5\$$ if we're not using a graph sheet and want to find everything mathematically?

• Are you sure the required zeta values are 0 and 0.5?
– Chu
Dec 30, 2020 at 20:05
• ω ≠ W. [filler] Dec 30, 2020 at 20:29
• For $\zeta=0$, this occurs when the radial line on the imaginary axis, or just find the gain as which the root locus intersects with the imaginary axis. For $\zeta=0.5$, you need to plot it in Matlab and search the intersection of the radial line with the root locus. In my code, this occurs at $K=112$ and for $\zeta=0, K=443$ Dec 30, 2020 at 23:43