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mm mm A block of mass m is attached to a wedge of mass M h M by a spring of natural length lo and spring constant k. The inclined frictionless surface of the wedge makes an angle a to the horizontal. The wedge is free to slide on a horizontal frictionless surface as shown in the figure. a) Write down all constraint relations on the particles? motion in cartesian coordinates. b) Show that the number s of degrees of freedom is 2 (. c) Choose s convenient generalized coordinates

mm mm A block of mass m is attached to a wedge of mass M h M by a spring of natural length lo and spring constant k. The inclined frictionless surface of the wedge makes an angle a to the horizontal. The wedge is free to slide on a horizontal frictionless surface as shown in the figure. a) Write down all constraint relations on the particles? motion in cartesian coordinates. b) Show that the number s of degrees of freedom is 2 (. c) Choose s convenient generalized coordinates

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A block of mass m is attached to a wedge of mass M h by a spring of natural length lo and M a spring constant k. The inclined frictionless surface of the wedge makes an angle a to the horizontal. The wedge is free to slide on a horizontal frictionless surface as shown in the figure. a) Write down all constraint relations on the particles? motion in cartesian coordinates. b) Show that the number s of degrees of freedom is 2 (. c) Choose s convenient generalized coordinatest d) Obtain the expression of the velocity of m with respect to O and show that Vm/o = xỉ + s7 e) Take the reference of potential energy at Ox axis Obtain the expression of the kinetic and potential energy (gravitational plus Elastic) of the system (wedge + block). ( f) Show that the Lagrangian function is given by: (M + m) L = 1 ン?、 +jms² + ma's'cos(a) – (s – lo) – mg(h – ssin(@)) specifying the origin of each term in the Lagrangian functio. g) Obtain expressions of the generalized momenta h) Derive the Euler - Lagrange equations (
Transcribed Image Text:A block of mass m is attached to a wedge of mass M h by a spring of natural length lo and M a spring constant k. The inclined frictionless surface of the wedge makes an angle a to the horizontal. The wedge is free to slide on a horizontal frictionless surface as shown in the figure. a) Write down all constraint relations on the particles? motion in cartesian coordinates. b) Show that the number s of degrees of freedom is 2 (. c) Choose s convenient generalized coordinatest d) Obtain the expression of the velocity of m with respect to O and show that Vm/o = xỉ + s7 e) Take the reference of potential energy at Ox axis Obtain the expression of the kinetic and potential energy (gravitational plus Elastic) of the system (wedge + block). ( f) Show that the Lagrangian function is given by: (M + m) L = 1 ン?、 +jms² + ma's'cos(a) – (s – lo) – mg(h – ssin(@)) specifying the origin of each term in the Lagrangian functio. g) Obtain expressions of the generalized momenta h) Derive the Euler - Lagrange equations (
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