Non-Ideal Transformer Equations
For Part A you should redraw the circuit like this: -



The extra inductances I've added are: -


(1 - k)L1
(1 - k)L2


These are the leakage inductances that will produce resonance. The 100% coupled parts serve only as an impedance transformer such that the secondary impedances (these)....


(1 - k)L2
C1
R4


... can be transferred to the primary via the 100% coupling. But you need to know how to transform those impedances and therefore, you need to know the turns ratio. The turns ratio is: -

$$\sqrt{\dfrac{kL2}{kL1}} = \sqrt{\dfrac{L2}{L1}}$$

Can you take it from here?

Part B (k = 0) is trivial because it just involves L1 and C2.