Neat and clean work neededPlot diagram if neededPlease do if you are 100 Percent confidential for accuracy Problem 3: Consider a critically damped oscillator. At time t = 0 it is sitting at its equilibrium positionand is kicked in the positive direction with velocity vo. Find and plot its position as a function of time.Do the same if it is released from rest at position x = xo. In this case, how far is it from equilibrium aftera time equal to the period it would have in the absence of damping?

Given: Case 1: At t=0 x=0 v=v0 Case 2: At t=0 x=x0 v=v0 To find: Plot its position as a function of…

Answered: Problem 3: Consider a critically damped…

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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For the system shown in the figure, set up the equation of motion for the mass, m, and solve for the steady state amplitude and phase angle.
For the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k = 2 N/m and f(t) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) Find the steady state maximum acceleration.
A mass of a 2 slug, when attached to a spring, causes an elongation of 2 ft in this spring and then comes to rest in the equilibrium position. Starting at t = 0 an external force equal to f(t) = 8 (sin (4t)) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force equal to 8 times the instantaneous velocity.
A particle of mass m attached to a rigid support by a support of constant k. At equilibrium, the spring hangs vertically. This mass-spring system is joined by another identical oscillator, whose spring is hung from the previous mass. Consider only the vertical movement. a) write the equations of motion of the coupled system b)Compute the normal mode frequencies for one-dimensional vertical oscillations and then show that the ratio of the two normal frequencies is √5+1/√5−1 c)Find the ratio of the amplitudes of the two masses in each separate mode. (You do not need to consider the force of gravity acting on the masses because it is independent of the displacements.)
PROBLEM #2:- Derive the equation of motion of the shown system, x is from static equilibrium position. Find the natural frequency, the critical damping (solve on given space)
Consider the given wing vibration model, determine the equations of motion of the system. Note that the “G” is the center of mass and “e” is the distance to the point of rotation.
Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.
Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?
A body weighing 5kg is attached to a very light bar as depicted below. The set-up is free to rotate in the vertical plane about pin support O. The force applied at point C makes the bar oscillate(via small rotation) about the position of equilibrium illustrated below Present the differential equation of motion to include the amplitude and the phase angle
Derive the expression for motion and determine the natural frequency of the system shown in the figure below. Neglect the mass of the rod.
Question 2 A pendulum consisting of a bar “B” and a mass “C” is suspended from a fixed pivot at “O” as shown in figure 2– a. A light spring is attached to the pendulum at point “P” and is anchored at a fixed point “Q”. When the pendulum is in equilibrium the line OC is at 450 from the vertical and the angle OPQ is 900. Calculate the natural frequency of the pendulum for small oscillations about the equilibrium position. The following data is available: Bar “B” Mass “C” Spring PQ mass 1 kg 6 kg centre of gravity G1 G2 radius of gyration about the centre of gravity 0,1 m 0,025 m spring stiffness 700 N/m
A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal spring is attached to the glider, and the other end is attached to the end of the track. When released, the glider oscillates in SHM with frequency 4.15 Hz. Find the period of the motion. Find the angular frequency of the motion. Find the force constant kk of the spring. Find the magnitude of the force that the spring exerts on the glider when the spring is stretched by 0.0200 m.

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