Consider the simple damped spring-mass system shown in the first figure. The mass is driven byan external fore given byF() = Fo cos(ut +)The mass is at rest at its equilibrium position, z-0, when the force is turned on instantaneouslyat t- 0. The response of the mass to this driving foree in shown in the second figure. Assumingthat the mass is m -1 kg, use the time series for z(t) to get estimates (within 20%) for:(a) The natural frequeney of the undamped oscillator, wo/(2) in Hz.Hint: You may assume that y is small, so that u = V - 7/4s u.(b) The damping coellicient, 6 in N s/m.(e) The frequency of the driving force, w/(27) in Hz.(d) The amplitude af the driving force, Fo in N.(e) What is o?y= 0.607, a = 2* 1, F, = 10, = x0.5, a, = 2 x 0.25.......10Time (s)1520(u) jueLueoedsig

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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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4G VOWIF O 450 J A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is A = 0.01 m and the mass of the block is m = 100 g then the angular frequency w is equal to 20 rad/s O 5 rad/s O 1.25 rad/s O 10 rad/s O 2.5 rad/s
Determine the response x(t) of the system in the figure, when the system is initially at rest, and k1= 100 N/m, k2 = 500 N/m, c = 20 Ns/m ja m = 89 kg.
PROBLEM3: - Derive the equation of motion and find the steady-state response of the system shown in Figure 3 for rotational motion about the hinge O for the following data: k₁ = k₂ = 5000 N/m, a = 0.25 m, b = 0.5 m, 1 = 1 m, M = 50 kg, m 500 N, w = 1000rpm. 10 kg, Fo F(t)= Fo sin cot Uniform rigid bar, mass m T esssst reelle Figure 3 |k₂ M
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
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.
The figure below shows a single degree of freedom control surface/actuator system. The control surface has a mass moment of inertia J = 30 kg.m2 about the hinge, the effective actuator stiffness and damping values are k = 3000 N/m and c = 500 Ns/m respectively and the rotation of the control surface is rad. The actuator lever arm has length a = 0.2 m. A force f (t) = 58 (t) N is applied to the control surface at a distance d = 1 m from the hinge. It is assumed that the main surface of the wing is fixed rigidly as shown in the figure. Assume small angle approximation. Determine the tip velocity (velocity at the location of f(t)) at t = 0.1 s 0(t) f(t) C 152.74 mm/s 499.47 mm/s 583.77 mm/s 400.63 mm/s 285.64 mm/s d
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The disk rolls without slip a. What is the critical damping coefficient, c for the system? b. Plot the response of the system when the center of the disk is displaced 5 mm from equilibrium and released from rest, if: i. c= cd/2 r= 40 cm 4 kN/m thin disk of mass m = 1 kg. no slip
ANSWER ALL QUESTIONS OTHERWISE DONT ATTEMPT IT STRICTLY.
Show this complete solution for this force driven without damping equation:
8. A control pedal of an aircraft can be modeled as the single - degree of freedom system of figure below. Consider the lever as a massledd shaft and the pedal as a lumped mass at the end of the shaft. Use the energy method to determine the equation of motion in and obtain the natural frequency of the system. Assume the spring to be unstretched at 0 = 0 and gravity points down. www 1/₂
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