Initially cylindrical drums \[P\] and \[Q\] were placed at equal distance \[L\] from center of mass \[C\] of the rough rod \[AB\] in horizontal position. The drums were spinning in opposite directions with angular velocities. The rod is displaced by distance \[x\] towards left and released so that it performs SHM. If difference in reactions at \[Q\] and \[P\] is \[\frac{mgx}{L}\] where m is the mass of the rod, find the time period of oscillations, if m is the coefficient of friction:

• A. \[2\pi \sqrt{\frac{L}{g}}\]
• B. \[2\pi \sqrt{\frac{(L-x)}{g}}\]
• C. \[2\pi \sqrt{\frac{(L+x)}{\mu g}}\]
• D. \[2\pi \sqrt{\frac{L}{\mu g}}\]