4.20. Assuming small angular oscillations, derive the differential equation ofmotion of the vibratory system shown in Fig. P4.5. If m1 = m2 = 0.5 kg,4 = 12 = 0.5 m, k = 10* N/m, c = 50N s/m, and F = 10 sin 5t N,determine the complete solution as a function of time for the initial conditions60 = 0 and 6o = 2 rad/s.F-m212Fig. P4.5

Given: Derive the differential equation of the motion.

Answered: 4.20. Assuming small angular…

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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Consider the dynamic system shown below. Rod Pulley Rc Rod Pulley RA = 10 cm PIB 1A The following parameters are given for the system: m₂ = 1 kg RA mg mc 2 kg RB Rc 20 cm m₂ = 3 kg R₂ = 30 cm k = 1200 N/m Note that pulleys A and B are constrained to move together and pulleys C and D are constrained to move together. Useful note... a. Obtain the characteristic equation(s) for this system. b. The applied force is removed. Then, pulley A/B is turned 2 degrees and released from rest. Find the system response.
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my''(t) +by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 20 kg, b = 80 kg/sec, k = 260 kg/sec², y(0) = 0.3 m, and y'(0) = -0.3 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point? (c) Find the frequency of oscillation for the spring system of part (a). (d) The corresponding undamped system has a frequency of oscillation of approximately 0.574 cycles per second. What effect does the damping have on the frequency of oscillation? What other effects does it have on the solution? (a) y(t) = plz answer a-d
3.21. What is the amplitude of steady-state oscillation of the 30-kg block of the system of Fig. 2000 sin 100N 4 x 106 N/m 40 kg =3 kg m2 cm 20 cm 30 kg Y 2700 N.s/m GURE P3.21 X = 1.52 mm
More than one answer is possible
Find: X2(s)/ F(s) Given: M1 = 2 Kg M2 = 4Kg K1 = 2N.s/m K2 = 1 N.s/m K3 = 4 N.s/m B1 = B2 = B3 = 2 N/m x1(t) fv, x2(t) f(t) K1 K3 M1 K2 M2 fv, (a) F(s) (Fr,s + K,) X,(s) Δ (b)
PART OF MECHANICAL VIBRATIONS SUBJECT USE VIRTUAL WORK The uniform bar shown in Fig. P3.6 has mass m, length l, and mass moment of inertia 1 about its mass center. The bar is supported by two springs kı and k2, as shown in the figure. Obtain the differential equation of motion and determine the natural frequency of the system in the case of small oscillations.
4.23 The design of the agitator in a washing machine is the object of an experimental study. One phase of the study deals with the relationship between the maximum torque T necessary to oscillate the agitator shaft and the associated parameters, which include the oscillation frequency f, the angular velocity w with which the agitator rotates during the oscillation, the diameter D of the agitator, the height h and the width w of the paddles, and the number N of paddles. Relate the maximum torque to the other variables in the problem. Viscous effects do not influençe the flow. The effect of the free surface is also unimportant. und thooed denshy p.
Fig. P4.6 4.22. Derive the differential equation of motion of the simple vehicle model shown in Fig. P4.7. The vehicle is assumed to travel over the rough surface with a constant vehicle speed v. Obtain also the steady state response of the vehicle. For this system, let m = 10kg, k = 4 x 103 N/m, c = 150N · s/m, i = 2 m, and the amplitude Yo = 0.1 m. Determine the maximum vertical displacement of the mass and the corresponding vehicle speed. Determine also the maximum dynamic force transmitted to the mass at the resonant speed. m 2πη y = Y, sin y Fig. P4.7
Please do not copy any answers already posted, they are incorrect.
cquar? 2.55. Determine the differential equation of motion and establish the critical damping for the system shown in Fig. P2.55. FIGURE P2.55. m₂ To
Mechanical Vibration Problem
For the system shown in figure below, derive the differential equation of motion for small oscillation. If m1=m2=1 kg, k1=k2=1000 N/m, c1=c2=10N·s/m, a=b=0.5 m, and l=1 m ﬁnd the solution after 1 s provided that the initial angular displacement is zero and the initial angular velocity is 5 rad/s. Assume that the rod is massless.

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