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*(a) A simple pendulum supported by a light rigid rod of length l is released fr

ID: 1655188 • Letter: #

Question

*(a) A simple pendulum supported by a light rigid rod of length l is
released from rest with the rod horizontal. Find the reaction at the
pivot as a function of the angle of inclination.
(b) For the cube of Problem 1, find the horizontal and vertical compo-
nents of the reaction on the axis as a function of its angular position.
Compare your answer with the corresponding expressions for the equiv-
alent simple pendulum.

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answer : (a) 3Mg cos; (b) (Mg/8)(9 sin 2, 11 + 9 cos 2), (3Mg/2)( sin 2, 1 + cos 2).

i need how to get answers

Explanation / Answer

a) for a light rigid rod supporting a pendulum of mass M
   at angle phi with horizontal
   loss in height of the pendulum = l(1 - cos(phi))
   loss in PE = Mgl(1 - cos(phi)) = gain in KE = 0.5Ml^2w^2
   Mgl(1 - cos(phi)) = Mw^2l^2
   where w is its angular velocity about pivot
   also, reaction force at pivot , F = Mg*sin(phi) - Mw^2*l [ where l is length of the rod]
   so, F = Mg*cos(phi) - 2Mg(1 - cos(phi)) = 3Mgcos(phi) - 2Mg