What I want to do, re my question of a time shifted resistor, is to analyze the input of a switching regulator consisting of the input capacitor with its ESR and the inductance of the trace maybe with or without the resistance of the trace. I am interested in the regulator switch-off transients where the load current is 5A, the regulator takes 15nsec (a SWAG) to turn off and the regulator is represented in the circuit as a 3 ohm load resistor. I am assuming a 24V DC input; C is 15uF with 1 ohm ESR; L is 0.05uH; I ignored the 7 mohm trace resistance. I can't figure out how (if possible at all) to set up a Laplace transform circuit that runs the 5A steady state for a short period, and then the 5A abruptly drops to zero. I want to understand the transient at the LC node. At the basic level about 8v reverse EMF is produced across the inductance, but instant voltage change is not allowed with a capacitor. Or if the high dv/dt is assumed you get current through the capacitor in the millions of amps. But then if current flows through the capacitor, the abrupt current drop through the inductance no longer exists removing the back EMF; and the dog keeps chasing its tail.
In any event I am unable to come up with a Laplace transform that accounts for the abrupt drop to zero of the load current through the inductance, and opens the load resistor. My first idea was the change the load resistor from 3 ohms to 10^12 ohms time shifted, but that fell apart.