Need Help To Express The Voltage! Tonight!

[Frida]

This is from a FET-transistor.


https://i.imgur.com/wRvB9.jpg
**broken link removed**

I would like to express Uut(t) with Ugs!

I would write it as: Uut(t)= gmUgs*(RL//Rs) but then the voltage amplification is not reasonable.

Thanks for the help!
/Frida

 

[panic mode]

what is on left side of the circuit (shows open)?
it looks like you are trying to solve small signal model for MOSFET.
show original circuit before reducing it to a small signal model.