Solving RLC Circuit Problem: Underdamped CKT Roots

[Isma]

i have a question where
s1,2=(-4 (+-) j3) 10^3
are roots of a second order D.E of a series RLC ckt
where s1,2=(-z (+-) (z^2 -1)
(z is zeta)
now from
s1,2=(-4 (+-) j3) 10^3 ,its showing roots of underdamped ckt(complex nd conjugate)
but when i solve eq. z gives 2 values(but z must be less than 1 nd gr8er than 0 acc. 2 condition of underdamped ckt)
help please

 

[SGT]

i have a question where
s1,2=(-4 (+-) j3) 10^3
are roots of a second order D.E of a series RLC ckt
where s1,2=(-z (+-) (z^2 -1)
(z is zeta)
now from
s1,2=(-4 (+-) j3) 10^3 ,its showing roots of underdamped ckt(complex nd conjugate)
but when i solve eq. z gives 2 values(but z must be less than 1 nd gr8er than 0 acc. 2 condition of underdamped ckt)
help please

The roots of a second order system are:
$$s_{1,2} = -\zeta \omega_n \pm j\omega_n \sqrt{1 - \zeta^2}$$
where $$\omega_n$$ is the undamped natural frequency and $$\zeta$$ is the damping coefficient.

 

[ravenprp]

It seems like you are trying to solve a second order differential equation for an RLC circuit, and you have found the roots to be s1,2=(-4 ± j3) 10^3. These roots represent the natural frequency of the circuit, which is determined by the values of R, L, and C in the circuit. The fact that these roots are complex and conjugate indicates that the circuit is underdamped, meaning that it will oscillate before reaching a steady state.

You are also trying to solve for the damping ratio, represented by zeta (ζ). However, you have encountered a problem where zeta can have two values, but it should only have one value for an underdamped circuit. This is because the condition for an underdamped circuit is 0 < ζ < 1. In this case, it seems like you may have made a mistake in your calculations or there may be some other factor affecting the results.

To solve this problem, you may need to go back and carefully check your calculations to ensure that you have not made any errors. You can also try using different methods or techniques to solve the differential equation, such as the Laplace transform or the method of undetermined coefficients. It may also be helpful to consult with a tutor or professor for further guidance and clarification.