Question

please show me or tell me a trick, on how can i tell right away when a characteristics equation(system) is

1)overdamped

2)underdamped

3)critically damped

4) nonlinear

show each an example

write neatly!!!!!

Answer 1

The only that is 100% sure shot is that comparing the characteristics equation with the given equation and more precisely by observing the middle term in the denominator of the characteristics equation i.e. 2w_n.

T.F= (k×w_n)/(s^{​​​​​​2} +2×w_n× +(w_{​​​​​​n})² ) ; characteristic equation:- s^{​​​​​​2}​​​​​+ 2×w_n××s +w​​​​_​​n²

Where w_{​​​​​​n} = undamped natural frequency, = damping factor.

Now as we know the conditions for different types of system i.e.

• For undamped system  =0
• For underdamped system. 0<<1
• For critically damped system  = 1
• For over damped system . >1

Now examples:-

There is no mention about non linear systems as I don't have any idea about that condition but apart from last condition given in the question for rest the above given descriptions is best suited. just remember the condition of for different system.