use the mesh-current method to find the steady-state expression for v0
IÖ = Ia - Ib
-400/0° + ( 50 + j300 )Ia – 50Ib – 150( Ia – Ib ) = 0 (KVL)
( 150 – j100)Ib – 50Ia + 150( Ia – Ib) = 0 (KVL)
Solving,
Ia = - 0.8 – j1.6 A
Ib = -1.6 + j0.8 A
V0 = 100Ib = -160 + j80 = 178.89/153.43° V
v0 = 178.89 cos( 5000t + 153.43° ) V