Is that SHM ?

Classical Mechanics Level 4

A uniform rod is placed on two spinning wheels ( $\omega = 20$ ) with the fixed axes separated by a distance $l$ as shown. The coefficient of friction between rod and wheel is $\mu$ . If rod perform SHM then find time period if not then answer 0.

Details and asumptions

$\bullet$ $\mu = 39.4784, l=80, g=10$

$\bullet$ All the values above are in SI units.

$\bullet$ Approximate answer to nearest integer.

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