Two problems on circuit analysis

Electric circuit analysis problems. See attached file for full problem description.

Complex coupled circuits

The circuit configuration chosen is that of a pair of tuned circuits which are coupled together and both primary and secondary are tuned to the same frequency. The primary has an inductance of 1 mH and the secondary has an inductance of 1.5 mH. The resistance of the primary is 10 ohms and the secondary 12 ohms. the secondary is terminated in a load resistance of 1K ohms. If the coupling coefficient between primary and secondary is 0.75 find the impedance looking into the primary terminals at a frequency of 15KHz The circuit is to be tuned over the given frequency range by means of capacitors which are connected in series with the primary and secondary. Calculate the capacitor range requi... click for more

A second order system satisfies the attached differential equation:

A second order system satisfies the attached differential equation: Calculate the natural complete response Xn(t) of the system, provided that: a0 = 13; a1 = 4; x(0) = 1; dx(o)/dt = 4. See attached file for full problem description.

In the attached circuit, using nodal analysis, calculate the mesh current I1 in the phasor domain

In the attached circuit, using nodal analysis, calculate the mesh current I1 in the phasor domain. I am having large problems in understanding the phasor domain. Please show work to help aid my understanding.

For the attached circuit, calculate the Thevenin equivalent volatge at terminals a-b

For the attached circuit, calculate the Thevenin equivalent volatge at terminals a-b.