1. For a single degree of freedom spring–mass–damper system with m = 1 kg, k = 4x104 N/m, and e = 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¬{»' (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. For a single degree of freedom spring–mass–damper system with m = 1 kg, k = 4x104 N/m, and e = 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¬{»' (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.

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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