Hello All,
Please can you assist me in my solution if it is correct. I need to know the basics if a negative resistor will change my node two equation? are my natural frequencies correct? More importantly how do u answer question 3? Please help. Thanks.

 

Hi,

I dont know if i will be able to get to 1 and 2, but for number 3 i will help a little now.

First, you should compute the response, and in doing so you should get a function with at least one exponential factor in it. Look at the exponential factor(s) and try to think about what is going to happen as time increases from 0 to some very long value.
Also, once you have the response since all the values are given you can just compute the results numerically over time and see how the response varies. If the response shoots up at any time and continues to rise, that means it is unstable (RHP).
To know the value of the period which would be sufficient you can examine the time constants and try to calculate for a longer period than that, say 100 times the longest time constant. You could go longer though, and if you like you can calculate several values to see how it is rising or falling or flattening out. From that you should be able to deduce what is happening here.

 

Where you are setting up your node 2 equation, you start with Iis - Ic - Ir0 = 0

This becomes 2 V1 - 2 Vs + V2/-1 = 0

Shouldn't this be 2 V1 - 2 Vs - V2/-1 = 0?