Non-resonant microwave absorption (NRMA) studies of superconducting $MgB_2$ and a sample containing $sim10$% by weight of MgO in $MgB_2$ are reported. The NRMA results indicate near absence of intergranular weak links in the pure $MgB_2$ sample. A linear temperature dependence of the lower critical field $H_c_1$ is observed indicating a non-s wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d wave symmetry is also not observed. In the $MgB_2+ MgO $sample, much larger low field dependent absorption is observed indicating the presence of intergranular weak links. The hysteretic behavior of NRMA is compared and contrasted in the two samples. In the pure $MgB_2$ sample, a large hysteresis is observed between the forward and the reverse scans of the magnetic field indicating strong pinning of flux lines. This hysteresis saturates a few degrees below $T_c$ while in the $MgB_2 + MgO$ sample, a much slower increase of hysteresis with decreasing temperature is observed, a signature of weaker pinning.
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