Answered: A mass-damper-spring system has the…

A mass-damper-spring system has the parameters m= 4.5 kg, c = 85 N s/m, k = 1750 N/m. At what frequency does the system vibrate? 14.25 rad/s 17.31 rad/s 19.72 rad/s O21.87 rad/s

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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A0.80 kg mass is attached to a light spring with a force constant of 42.9 Nim and set into oscillation on a horizontal frictionless surface. (Hintl: The angular frequency, s of an ideal mass-spring system is given by w = VK. Where kis the spring constant, and m is the mass value, Hint2: The maximum displacement is the amplitude A. the maximum velocity is u4, and the maximum acceleration is aA.) If the spring is stretched 5.0 cm and released from rest, determine the following. (a) maximum speed of the oscillating mass See if you can find an expression which relates the maximum speed of the oscillating mass to known values, m/s (b) speed of the oscillting mass when the spring is compressed 1.5 cm from the equilibrium position Is energy conserved for this oscillating system? mis () speed of the oscillating mass when the spring is stretched 1.5 cm from the equilibrium position When the mass-spring system is oscilating, how does the speed of the oscillating mass when the spring is…
The amplitude of vibration of a single degree of freedom spring-mass-damper system is observed to reduce to 15 % of its initial value after 5 cycles. Spring stiffness equals (1500 + 21) N/m and mass equals (7.5 + 21) kg. Determine: • The undamped natural frequency; • The damped natural frequency; • The logarithmic decrement; • The damping ratio; and • The coefficient of damping.
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PARTS A & B solve carefully and label each part and CIRCLE FINAL ANSWER ( Use image Below) Part A - Assuming the elements are all linear, determine a model for the mass-spring-damper system. Make sure to clearly define the direction of positive velocity. Simplify your answer such that the model is in terms of the parameters (?, ?, ??, ??), the input force (?), the spring deflection and the mass velocity as well as their time derivatives. Part B - Take the ANSWER from PART A and replace the damping constant ? with the nonlinear expression ? = ?? + ?? + ? , with ? as the velocity of the mass.
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2. Consider the spring mass damper system shown on the next page with m1 | m2 = 1 kg, k = 1 N/m, and b= 1 N/(ms). Note that you can neglect gravity by considering deviations from the system at rest. F(1) M m wwwww k
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