Transcription of Question 3–12
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Example: biology
Question 3–12
105 Question 3 12A particle of massmis attached to a linear spring with spring constantKandunstretched lengthr0as shown in Fig. P3-12. The spring is attached at its otherend at pointPto the free end of a rigid massless arm of lengthl. The armis hinged at its other end and rotates in a circular path at a constant angularrate . Knowing that the angle is measured from the downward directionand assuming no friction, determine a system of two differential equations ofmotion for the particle in terms ofrand . tlmrKOP Figure P3-12 Solution to Question 3 12 KinematicsFirst, letFbe a fixed reference frame. Then, choose the following coordinatesystem fixed in reference frameF:Origin atOEx=AlongOPWhent=0Ez=Out of PageEy=Ez ExNext, letAbe a reference frame fixed to the arm. Then, choose the followingcoordinate system fixed in reference frameA:Origin atOex=AlongOPez=Out of Page(=Ez)ey=ez exFinally, letBbe a reference frame fixed to the direction along which the springlies ( , the directionPm).
105 Question 3–12 A particle of mass m is attached to a linear spring with spring constant K and unstretched length r0 as shown in Fig. P3-12. The spring is attached at its other end at point P to the free end of a rigid massless arm of length l.The arm is hinged at its other end and rotates in a circular path at a constant angular
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