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A rod of lengths L is supported two ideal strings of length l such that the system hangs in a vertical plane. Case 1: Rod is kept horizontal displaced slightly perpendicular to the plane and allowed by oscillate. Case 2: Rod is given a small twist about central axis and then allowed to oscillate. Let T_(1), T_(2) be the period of oscillations in the two respective cases. |
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Answer» `T_(1)=2pisqrt(l/g)` `-(2Tphi) L/2=(mL^(2))/12 (d^(2)theta)/(dt^(2))` `IMPLIES(d^(2)theta)/(dt^(2))=-((6g)/L)phi` or `(d^(2)theta)/(dt^(2))=-((3g)/l)theta` `impliesT_(2)=2pisqrt(l/(3g))` 
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