solve, show solution and matlab code, vibrations An impact force is used to manually apply an impulse to a model of a single degree-of-freedom system with a mass of 3 kg, stiffness of 12 N/m, and damping coefficientof 6 N-s/m, and subject to the initial conditions x(0) =0.01 m and v(0) = 1 m/s.A double impact of the form,f(t) = 38(t) + 8(t − 1)Determine and plot the system total response of the system.

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Answered: An impact force is used to manually…

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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A single degree of freedom mass-spring-viscous damper system with mass m, spring constantk and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is q = 2km q = 2/ km 2k = b m k q =2
you are given the mass, damping, andspring constants of an undriven spring-mass systemmy'' + μy + ky = 0.You are also given initial conditions. Use a numerical solverto(i) provide separate plots of the position versus time (y vs.t) and the velocity versus time (v vs. t),(ii) provide a combined plot of both position and velocity versus time, and(iii) provide a plot of the velocity versus position (v vs. y) inthe yv phase plane. a. m = 1 kg, μ = 0 kg/s, k = 9 kg/s2, y(0) = 3 m,y'(0) = 2 m/s b.m = 4 kg, μ = 4 kg/s, k = 1 kg/s2, y(0) = 3 m,y'(0) = 1 m/s
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A mass of one kg stretches a spring 49 cm in equilibrium. It is attached to a dashpot that supplies a damping force of 4 N for each m/sec of speed. Find the steady state component of its displacement if it's subjected to an external force F(t) = 8 sin(2t) — 6 cos(2t) N. Note: The steady state component of the displacement is the solution obtained by setting all derivatives equal to zero. Therefore, in this case it is of the same form as the right-hand side of the ODE, that is, y(t) = A cos(2t) + B sin(2t). Just find A and B. y(t)
Q2 The angular position c of a mass is controlled by a servo system through a referen signal °r. The moment of inertia of moving parts referred to the load shaft, J, is 150 kebo and damping torque coefficient referred to the load shafi(B, is 4.5 x 103 Nw-m fraden The torque developed by the motor at the load s 7.2 x 10* Nw-m per radian of error (a)Obtain the response of the system to a step input of 1 rad and determine the peak time, peak overshoot and frequency of transient oscillations. Also find the steady state error for à constant angular velocity of 1 revolution / minute. (b)If a steady torque of 1000 Nwm is applied at the load shaft, determine the steady Kan state error. 5(J5+ B) 03 For the system shown, apply a proportional controller to move the time constant to a sixth of its open loop value. R(s) + E(s) U(s) Kp 'Y(s) s +0.333 10
2- A damped single degree of freedom mass-spring system has a mass m = 5 kg, a spring stiffness k = 3,125 N/m, and a damping coefficient c = 25 N. s/m. The mass is subjected to a harmonic force which has an amplitude F₁ = 20 N and frequency w₁ = 10 rad/s. The initial conditions are such that x0 = 2 cm and v₁ = x = 0 m/s. Determine the displacement, velocity, and acceleration of the mass after t = 1 s. Determine the magnification factor and phase angle.
A boxcar moving at 1.7 m/s hits the shock absorber at the end of the track. The boxcar mass is 20,000 kg. The stiffness of the absorber is k = 100,000 N/m, and the damping coefficient is c = 40,000 N-s/m. The box car and shock absorber act as one system for a brief period while in contact. a. Make dynamic model (define system equation) for the boxcar and shock absorber system. Then, numerically simulate the system response starting at the point of contact and ending after 6 seconds. Plot the spring force, boxcar velocity, and boxcar displacement as functions of time. b. State the maximum spring deflection. Note that once the boxcar loses contact, the model is no longer valid. Model is not valid for the entire 6 seconds. At what point in time is contact lost? c. What is the boxcar velocity when contact is lost? H m ====== k
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4) Figure below shows a spring-mass- damper system. The mass is subjected to a steady force of P 2 N. The spring constant k 200 N/m, the mass m 5.2 kg and the damping ratio is f= 12.2 N. sec/m. What is the position of the mass after a sufficiently long time of force application? You may assume that the mass is initially at rest, and the spring at time t = 0 is in its unstretched condition. m k

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