Measuring the damping frequency from an oscilloscope reading

[Boltzman Oscillation]

Homework Statement:

From the oscilloscope reading, find the undamped frequency of oscillation, damped exponent, and damped frequency of oscillation if the damping ratio is .1.

Relevant Equations:

shown below

I know the following equations for if the damping ratio is less than 1: $$\sigma = -\zeta \omega_n$$ $$\omega = \sqrt{(1 - \zeta ^2)\omega^2_n}$$

I am given the following circuit that I built on LTSpice:

Measuring the voltage between node 2 and ground (blue), and the voltage Vc4(t) (green) I get the following reading:

what is the undamped frequency of oscillation, damped exponent, and damped frequency of oscillation? All I really need is the undamped natural frequency because I will be able to use the formulas to find the rest. How can I find it? Is it just the frequency of the green signal? Vc4(t)?

 

[Anachronist]

The frequency of the green squiggle is the damped frequency of oscillation. You'd have to use your equation to solve for the undamped frequency.

 

[Boltzman Oscillation]

The frequency of the green squiggle is the damped frequency of oscillation. You'd have to use your equation to solve for the undamped frequency.

Ah I guessed as much. In a critically damped scenario i get the following reading:

this time the blue line is my capacitor voltage. I am asked for the undamped frequency, is this just the frequency of the rising portion of the signal?

 

[cnh1995]

I am asked for the undamped frequency, is this just the frequency of the rising portion of the signal?

It is the natural frequency of the circuit i.e. the frequency with which the output would oscillate had there been no damping element(s).

 

[Boltzman Oscillation]

It is the natural frequency of the circuit i.e. the frequency with which the output would oscillate had there been no damping element(s).

Ah so without the resistors.

 

[cnh1995]

Ah so without the resistors.

Yes, but you can't find it by removing the resistors in the original circuit. The natural frequency term appears automatically in the transfer function.

 

[Anachronist]

Possibly this discussion might help.