k fnf E A mass m is attached to a wall with a spring of...

  

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k₁ fünf E μ A mass m is attached to a wall with a spring of stiff- ness k₁. The mass is free to slide on a surface with a dynamic coefficient of friction (ignore static fric- tion). The mass is attached to a pulley with mass, M, and outer radius r at a radius of r. This pulley is attached to two springs with stiffness, k₂ and k3, that are in parallel. (a) Determine the equation of motion of the sys- tem in terms of the angle of rotation of the pulley, 0. (b) Find the angular displacement of the rod, 0(t), for the initial conditions: 0(0)= and = 0. Assume that my = 1 kg, m₂ = 2 = kg, M = 0.5 kg. m = 2 kg. k₁= 200 N/m, k₂k3= 30 N/m, = 0.4 en r = 0.25 m. (c) Draw a plot of the system response to deter- mine how long the vibration will take to stop. (d) Now assume that the mass is able to slide on the surface without friction and use the en- ergy method to determine the system's equa- tion of motion and the natural frequency. k₂ 5 www M,r E k3 k₁ fünf E μ A mass m is attached to a wall with a spring of stiff- ness k₁. The mass is free to slide on a surface with a dynamic coefficient of friction (ignore static fric- tion). The mass is attached to a pulley with mass, M, and outer radius r at a radius of r. This pulley is attached to two springs with stiffness, k₂ and k3, that are in parallel. (a) Determine the equation of motion of the sys- tem in terms of the angle of rotation of the pulley, 0. (b) Find the angular displacement of the rod, 0(t), for the initial conditions: 0(0)= and = 0. Assume that my = 1 kg, m₂ = 2 = kg, M = 0.5 kg. m = 2 kg. k₁= 200 N/m, k₂k3= 30 N/m, = 0.4 en r = 0.25 m. (c) Draw a plot of the system response to deter- mine how long the vibration will take to stop. (d) Now assume that the mass is able to slide on the surface without friction and use the en- ergy method to determine the system's equa- tion of motion and the natural frequency. k₂ 5 www M,r E k3

Answer rating: 100% (QA)

a The equation of motion of the system can be found by applying Newtons second law of motion We can write it as follows F ma Where F is the force acti... View the full answer