My question is: for t>0, Should I treat the depentent 4io source as zero since the current io indicated on the figure is zero ?

Any help is appreicated.

 

I think so. That would nullify the current source and leave only the middle voltage source to power the circuit after the switch is flipped.

 

My question is: for t>0, Should I treat the depentent 4io source as zero since the current io indicated on the figure is zero ?

Any help is appreicated.

Yes, make sure you replace it by a short, because its going to effectively short out the rightmost portion of your circuit.

 

Jegues has corrected me. I mistook the dependant source for a current one, while it is a voltage source. Shorting it is mandatory.