need help solving these problems

Ghee
timer Asked: Jul 9th, 2018

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please do not copy from chegg or use other source like snapqa and make you handwriting clear as much as possible

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2. A 125 kg mass is attached to the end of a fixed-free beam of length 2.5 m as shown. A spring and viscous damper are attached to the end of the beam. (a) (15 points) What is the damping coefficient of the viscous damper such that the system's logarithmic decrement is 2.17 Call this value of the damping coefficient, (b) (20 points) The system is given a displacement of 5 mm and released. Determine the resulting time dependent motion of the mass if the damping coefficient isg. (c) (15 points) For the system in part (b) how long does it take to execute one cycle of motion? (d) (15 points) For the system in part (b) what is the amplitude at the end of the first cycle? (e) (20 points) The system is given a velocity of 5 m/s when it is equilibrium. If the damping coefficient is 5c, how long before the system achieves its maximum displacement? (f) (15 points) For the system in part (e) how long does it take for the system to have a velocity of 1 m/s? 2.5 m 125 kg E=210x10°N/m? I=6.3x106m k=3x105 N/m k LUC 3. (a) (80 points) Use the equivalent system method to derive the differential equation governing the motion of the system shown. Use r the downward displacement of the block of mass 3m as the generalized coordinate. The disks move without slipping relative to one another. (b) (20 points) What are the natural frequency and damping ratio of the system? M(t) 51 kar 3r T 3m m IC с C с
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