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ilovepdf.com_split_4 - 113 Question 322 A particle of mass...

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Unformatted text preview: 113 Question 322 A particle of mass m is attached to a linear spring with spring constant K and un- stretched length r as shown in Fig. P3-22. The spring is attached at its other end to a massless collar where the collar slides along a frictionless horizontal track with a known displacement x(t) . Knowing that gravity acts downward, determine a system of two differential equations in terms of the variables r and that describe the motion of the particle. x(t) g m r A B K O P Figure P3-22 Solution to Question 322 Kinematics First, let F be a reference frame fixed to the track. Then, choose the following coordi- nate system fixed in reference frame F : Origin at Q When x = E x = To The Right E z = Out of Page E y = E z E x Next, let A be a reference frame fixed to the direction of QP such that Q is a point fixed in reference frame A . Then, choose the following coordinate system fixed in reference frame A : Origin at O e r = Along QP e z = Out of Page e = E z e r 114 Chapter 3. Kinetics of Particles The geometry of the bases { E x , E y , E z } and { e r , e , e z } is shown in Fig. 3-18. Using Fig. 3-18, we have that E x = sin e r + cos e (3.485) E y = - cos e r + sin e (3.486) e r e E x E y e z , E z Figure 3-18 Geometry of Bases { E x , E y , E z } and { e r , e , e z } for Question 322....
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ilovepdf.com_split_4 - 113 Question 322 A particle of mass...

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