$18\mathrm{.}34$ The linear transformer in the circuit shown in Fig. P$18\mathrm{.}34$ has a coefficient of coupling of $0\mathrm{.}75.$ The transformer is driven by a sinusoidal voltage source whose internal voltage is $v_g=80cos400tV.$ The internal impedance of the source is $5+j0.$

a$)$ Find the frequency$-$domain a parameters of the linear transformer.

b$)$ Use the a parameters to derive the Th$$venin equivalent circuit with respect to the terminals of the load.

c$)$ Derive the steady$-$state time$-$domain expression for $v_2.$

Figure P$18\mathrm{.}34$