1. (32 points) For a single degree of freedom spring-mass-damper system with m = 1 kg,...

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1. (32 points) For a single degree of freedom spring-mass-damper system with m = 1 kg, k= 4x104 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 in the form x(t) = e-Coat (A cos(@at) +B sin(@at)) mm. (c) Plot the first ten cycles of motion. (d) Calculate the viscous damping value, c (in N-s/m), to give the critically damped case for this system. 1. (32 points) For a single degree of freedom spring-mass-damper system with m = 1 kg, k= 4x104 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 in the form x(t) = e-Coat (A cos(@at) +B sin(@at)) mm. (c) Plot the first ten cycles of motion. (d) Calculate the viscous damping value, c (in N-s/m), to give the critically damped case for this system.

Answer rating: 100% (QA)

Solution C i have employed MATLAB to d... View the full answer