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ilovepdf.com_split_4 - 113 Question 3–22 A particle of...

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Unformatted text preview: 113 Question 3–22 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 θ that describe the motion of the particle. x(t) g m r A B K O P θ Figure P3-22 Solution to Question 3–22 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 θ = 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 θ , e z } is shown in Fig. 3-18. Using Fig. 3-18, we have that E x = sin θ e r + cos θ e θ (3.485) E y = - cos θ e r + sin θ e θ (3.486) e r e θ E x E y e z , E z θ θ Figure 3-18 Geometry of Bases { E x , E y , E z } and { e r , e θ , e z } for Question 3–22....
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This note was uploaded on 04/03/2012 for the course AERO 310 taught by Professor Chakravorty during the Spring '07 term at Texas A&M.

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ilovepdf.com_split_4 - 113 Question 3–22 A particle of...

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