1)For the mechanical system shown, m = 1 kg and k = 600 N/m. Derive the expression for the peakamplitude ratio M, and resonant frequency w, for any arbitrary value of c. Generate a plot for w, vs. c,and another plot for M, vs. c, and explain how changing the damping in the system affects theseparameters. Make your plots for 0 ≤ c≤ 30 N.s/m.m12xwwwK

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Answered: 1)For the mechanical system shown, m =…

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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analytical mechanics
vibrations, please help
: An undamped oscillator has a natural frequency of a rad/s. Damping is added to the system to give a damping factor equal to 0.30 s¬1. Find the corresponding Q – value and frequency of damped oscillations. 3 For a Damped Simple Harmonic Oscillator, wo? – w² = 10-w,?, where (w) is the frequency of DHO. Find Q, and the logarithmic decrement (A) of the system. If wo = 106 rad/s, Q, = 5 × 10² and m = 10-10kg, calculate the stiffness, and resistive constant (b) of the system. S For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force F4 = bv : ngular frequency (w) is given by: E = nbwA². 1
Figure below shows a single degree of freedom system. The system has a moment of inertia I =37 kg.m² about point O, the stiffness and damping values are k =548 N/m and C =113 N.s/m, respectively. Considering a =1.6 m and b =0.7 m, find the damped natural frequency of the system in rad/s. a b C www
QUESTION 3 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K K MA M 0000 M F(1) F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M. at the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = Klk. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. What is the fundamental frequency (first natural frequency) of the modified system in rad/s? Use scientific notation with 3 signifincant figures. Omit…
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