Question

1. For a single degree of freedom spring mass-damper system with m = 1 kg; k = 4x10^4 N/m; and c = 10 N-s/m; complete the following for the case of free vibration: (a) Calculate the natural frequency (in rad/s), damping ratio, and damped natural frequency (in rad/s). (b) Given an initial displacement of 5 mm and zero initial velocity, write the expression for the underdamped free vibration as x(t) = e^(-Î¶Ï‰nt)(Acos(Ï‰dt) + Bsin(Ï‰dt)) mm. (c) Plot the first ten cycles of motion. Calculate the viscous damping value (in N-s/m) to give the critically damped case for this system.

          1. For a single degree of freedom spring mass-damper system with m = 1 kg; k = 4x10^4 N/m; and c = 10 N-s/m; complete the following for the case of free vibration:
(a) Calculate the natural frequency (in rad/s), damping ratio, and damped natural frequency (in rad/s).
(b) Given an initial displacement of 5 mm and zero initial velocity, write the expression for the underdamped free vibration as x(t) = e^(-Î¶Ï‰nt)(Acos(Ï‰dt) + Bsin(Ï‰dt)) mm.
(c) Plot the first ten cycles of motion.
Calculate the viscous damping value (in N-s/m) to give the critically damped case for this system.

Added by Kristi W.

Question

Please give Ace some feedback