![A slender uniform rigid bar of mass ๐ is hinged at O and supported by two springs, with stiffnesses 3๐ and ๐](https://www.gkseries.com/blog/wp-content/uploads/2023/09/A-slender-uniform-rigid-bar-of-mass-๐-is-hinged-at-O-and-supported-by-two-springs-with-stiffnesses-3๐-and-๐.jpg)
Q. A slender uniform rigid bar of mass ๐ is hinged at O and supported by two springs, with stiffnesses 3๐ and ๐, and a damper with damping coefficient ๐, as shown in the figure. For the system to be critically damped, the ratio ๐/โ๐๐ should be
![](https://www.gkseries.com/blog/wp-content/uploads/2023/09/Screenshot-710-1.png)
Ans: 4โ7
Sol:
![](https://www.gkseries.com/blog/wp-content/uploads/2023/09/Screenshot-711.png)