# Part a we start by analyzing the torques acting on

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Part AWe start by analyzing the torques acting on the rod when it is deflected by a small anglefrom the vertical. Consider firstthe torque due to gravity. Which of the following statements most accurately describes the effect of gravity on the rod?Choose the best answer.ANSWER:Assume that the spring is relaxed (exerts no torque on the rod) when the rod is vertical. The rod is displaced by a small anglefrom the vertical.Under the action of gravity alone the rod would move to a horizontal position. But for small deflections from thevertical the torque due to gravity is sufficiently small to be ignored.Under the action of gravity alone the rod would move to a vertical position. But for small deflections from thevertical the restoring force due to gravity is sufficiently small to be ignored.There is no torque due to gravity on the rod.θτθsin (θ)θcos(θ)1CorrectPart BFind the torquedue to the spring. Assume thatis small enough that the spring remains effectively horizontal and youcan approximate(and).θ
Express the torque as a function ofand other parameters of the problem.Hint 1.Find the change in spring lengthδDeflecting the rod will stretch or compress the spring by a length. The spring will react with a restoring forceθδ
5/26/16, 12:58 PMhomework #1given by Hooke's law:.What is ?Express your answer in terms of andHint 1.Relation between displacement and rotation angleConsider an object at a distancefrom the pivot it is rotating about. If it rotates through an angle, thenits displacementis given by.F=kδδlθrϕxx=rϕ.2
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CorrectHint 2.Find the moment armThe torqueabout a point is defined as the product of the forceacting on a body times the moment arm(perpendicular distancefrom the line of action of the force to the center point):What isfor the given situation?
Express your answer in terms of quantities given in the problem introduction.2l4
5/26/16, 12:58 PMhomework #1Page 22 of 33CorrectSince the torque is opposed to the deflectionand increases linearly with it, the system will undergo angular simpleharmonic motion.Part CWhat is the angular frequencyof oscillations of the rod?Express the angular frequency in terms of parameters given in the introduction.Hint 1.How to find the oscillation frequencycan be found from the equation of motion by comparing it to the standard form.This equation describes any angular simple harmonic motion. Bring your equation of motion into this standardform, and hence extract the expression forin terms of the parameters of this specific problem.

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