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

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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.
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A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f =3.185 hz. At a position x1, the object has a kinetic energie of 0,7 j and a potential energy 0,3 j. The amplitude oscillation,A,is?
Underdamped Mass-Spring System Find and graph the motion of a damped mass-spring system with mass m = 0.25 slugs, spring constant k = 4 lb/ft. and damping constanl b = I lb sec/fl. The mass is initially pulled to the right s1re1ching the spring by I ft. and th:n released.
The spring-damper-mass system shown in Figure Q3(c) is at rest when strict bya hammer with an initial velocity of 0.4 m/s causing the mass to move upwards.Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient ofviscous damping c = 0.6 Ns/m.(i) Determine the damped frequency of the spring-damper-mass system.(ii) Base on the given conditions derived in Q3(c)(i) and parameters givenabove, describe how you would derive the equation of motion ofdamped-free vibration.
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
2.7. Find the frequency equations for small oscillations of the systems shown. ! || min www m (a) m P
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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)
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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.

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