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A particle of mass m in suspended at the lower end of a thin negligible mass. The upper end of the rod is free to rotate in the plane of the page about a horizontal axis passing through the point O. The spring is underformed when the rod is vertical as shown in fig. If the period of oscillation of the system is pisqrt((L)/(n)), when it is slightly displaced from its mean position then find n. Take k = (9mgKL)/(l^(2)) and g = 10m//s^(2). |
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Answer» For small displacement `X = l sin THETA` `kx = kl sin theta` Torque about point `O = I_(o)ALPHA` `(kx)l + mg sin theta l = mL^(2)alpha` ltbr. `alpha = ((kl^(2) + mgL)sintheta)/(mL^(2))` For small `theta` `alpha = -[(kl^(2) + mgL)/(mL^(2))]theta` Time period `T = 2pisqrt((mL^(2))/(kl^(2) + mgL)) = pisqrt((L)/(25))` 
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