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meun y a damper with damping coefficient e, as well as a spring wi /m. Moment of inertia of the pulley is / = 0.01 kg m² and the: 2.1 m. The spring remains unstretched when mass m, is released = 0, then it oscillates in vertical direction. Note that the cable do against motion and the friction between the slider and the inclim ee-body diagrams of mass m, and pulley J; the ordinary differential equation (ODE) of this vibration system i

meun y a damper with damping coefficient e, as well as a spring wi /m. Moment of inertia of the pulley is / = 0.01 kg m² and the: 2.1 m. The spring remains unstretched when mass m, is released = 0, then it oscillates in vertical direction. Note that the cable do against motion and the friction between the slider and the inclim ee-body diagrams of mass m, and pulley J; the ordinary differential equation (ODE) of this vibration system i

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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6. Figure 8 shows a damped spring-mass system that contains a fixed pulley, a slider and a mass. There is a string whose one side is hung vertically by a mass m, = 1 kg. the other side connect to a slider m, = 05 kg which can slide along the incline (A = 30°). The center of slider is pulled by a damper with damping coefficient e, as well as a spring with force constant k = 2 N/m. Moment of inertia of the pulley is / = 0.01 kg m? and the radius of the pulley is r = 0.1 m. The spring remains unstretched when mass m, is released from rest at the position x = 0, then it oscillates in vertical direction. Note that the cable do not slip, the air resistance against motion and the friction between the slider and the incline can be neglected. i) Draw the free-body diagrams of mass m, and pulley /; i) Formulate the oardinary differential equation (ODE) of this vibration system in terms of x; i) Determine the damping coefficient e such that the system is being subcritical damped; iv) Given the damping coefficient e = 0.5 N- s/m, a) Find the equilibrium position, x. of mass. b) Determine the displacement of mass m, as a function of time www =30° Figure 8. (15 marks)
Transcribed Image Text:6. Figure 8 shows a damped spring-mass system that contains a fixed pulley, a slider and a mass. There is a string whose one side is hung vertically by a mass m, = 1 kg. the other side connect to a slider m, = 05 kg which can slide along the incline (A = 30°). The center of slider is pulled by a damper with damping coefficient e, as well as a spring with force constant k = 2 N/m. Moment of inertia of the pulley is / = 0.01 kg m? and the radius of the pulley is r = 0.1 m. The spring remains unstretched when mass m, is released from rest at the position x = 0, then it oscillates in vertical direction. Note that the cable do not slip, the air resistance against motion and the friction between the slider and the incline can be neglected. i) Draw the free-body diagrams of mass m, and pulley /; i) Formulate the oardinary differential equation (ODE) of this vibration system in terms of x; i) Determine the damping coefficient e such that the system is being subcritical damped; iv) Given the damping coefficient e = 0.5 N- s/m, a) Find the equilibrium position, x. of mass. b) Determine the displacement of mass m, as a function of time www =30° Figure 8. (15 marks)
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