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Question

A small ball of mass M is attached to the end of a uniform rod of equal mass M and length L that is pivoted at the top. Determine the tensions in the rod (a) at the pivot and (b) at the point P when the system is stationary. (c) Calculate the period of oscillation for small displacements from equilibrium and (d) determine this period for L = 2.00m .
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Solution

(a) At the pivot , F=Mg+Mg=2 Mg
(b) F=Mg(yL)+Mg=Mg(1+yL)
(c) T=4π32Lg
(d) For L=2.00 m,T=2.68 s

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