I am a bit stuck for part 1 of this exercise with unit analysis and keep on going around in circles by substituting these units in the ODE. If someone could answer this question ASAP, it would be highly appreciated.
Preview: Analysing the units of each terms in the ODE, give a relation between H, s and Ω, and another relation between Ω, F and s.
ODE = LI′′(t) + RI′(t) + 1 I(t) = G(t)
where L is the inductance (unit: henrys (H)), R is the resistance (unit: ohms (Ω)), C is the capacitance (unit: farads (F)), and G is the forcing term generated by an AC power (G is actually the derivative with respect to time of the AC voltage). The current is measured in amperes (A), and the time t in seconds (s).
All terms in a sum must have the same units. So, for example the last term is measured in Amperes divided by Farads. The first derivative means an extra division by seconds, so the second derivative means division by seconds squared. Can you continue?