A PIVOTING ROD ON A SPRING MASTERING PHYSICS

A slender, uniform steel rod of mass
and also size
is pivoted without friction about an axiswith its midpoint and also perpendicularto the rod. A horizontalspring, assumed massmuch less and with force continuous
, is attached to the lower end of the rod, withthe various other finish of the spring attached to a rigid support.

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(a) We start by analyzing the torques acting on the rod when it isdeflected by a tiny angle
from the vertical. Considerinitially the torque as a result of gravity. Which of the complying with statementsthe majority of accurately defines the effectof gravity on the rod?
 Under theaction of gravity alone the rod would certainly move to a horizontalplace. But for smalldeflections from the vertical the torquebecause of gravity is sufficiently little to be ignored. Under theaction of gravity alone the rod would certainly move to a vertical place.But for little deflectionsfrom the vertical the restoring pressure dueto gravity is sufficiently tiny to be ignored. There is notorque because of gravity on the rod.
(b) Find the torque
as a result of the spring. Assume that
is small sufficient that the springcontinues to be properly horizontal andyou have the right to approximate
(and
).Express the torque as a role of
and various other parametersofthe problem.(c) What is the angular frequency
of oscillations ofthe rod?Expush the angular frequency interms of parameters offered in the advent.Thanks