PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) = {1} cm. v (0) = ܠܠܠܠܠܠܠܝ 00000 k m Sec m 00000 k x1 (1) 5k 0000 m Figure 3 00000 k x₂ (1) 6000 kN/m. m 00000 k x3 (1) ܠܠܠܠܠܠܝ

PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) = {1} cm. v (0) = ܠܠܠܠܠܠܠܝ 00000 k m Sec m 00000 k x1 (1) 5k 0000 m Figure 3 00000 k x₂ (1) 6000 kN/m. m 00000 k x3 (1) ܠܠܠܠܠܠܝ

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

See similar textbooks

Similar questions

PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) m (2) {2} cm. = cm, v (0) Sec 00000 m k 00000 k x₂ (1) 5k 0000 Figure 3 00000 k x₂ (1) m 00000 k X3 (1)
PROBLEM5: a)Find the natural frequencies and mode shapes of the system shown in Figure 5. b) Find the free-vibration response of the two-degree-of-freedom system shown in Figure 5 with the initial conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0. Good luck h 2h 2k 2k mmm 2m 0.5K k mm Figure 5 m Tu2 0.5K Tul k mm
An advertisement board was pulled from the top point with a horizontal force of 100 kN with the help of a jack and subjected to 75 mm horizontal displacement. when the force is released suddenly, the time elapsed at the end of the 5th oscillation was measured as 1.50 seconds and the amplitude as 30 mm. 75 mm a ) Find the damping ratio of the system. b ) Find the natural vibration period Tn of the system and the damped period Td of the system. c ) Find the horizontal translational stiffness of the system.
The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly. C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).
(machine dynamic ) The mass(20 kg)-damper-spring system given in the figure on the right is under a harmonic force. a- Obtain the equation of motion by making the necessary assumptions for this system.b- Find and interpret the natural frequency, damping state (critical etc.), damping constant and damping degrees of the system using the values given in the table.c- Compare the situation at t=5s and t=20s. What changes have occurred?
Exercise The figure below shows a cable-suspended rigid beam. The beam carries a box that may slide relative to the beam when it vibrates and rotates 0 (t) about its center of gravity, c. Write the equations of motion of the system. You may use Lagrange's equations or any other equivalent method. Solve the equations of motion assuming the free vibration case. Cables. m k k2 J, mj k1 k1 uw Lwww
The figure shows a vibratory system with two degrees of freedom; the OA bar is rigid and homogeneous of mass m = 6 kg and length l = 2 m.Suppose that:c1 = 200 kN s/mc2 = 600 kN s/mk1 = 500 N/mk2 = 300 N/m a) Determine the equations of motion of the system. b) Determine the matrices associated with the vibratory system. c) Determine the natural frequencies.
1: the mass damper spring given in the figure on the side is a harmonicit's under the influence of force. a-) obtain the equation of motion by making the necessary admissions for this system. B - ) natural frequency of the system using the values given in the table, damping State (critical, etc. ), find and interpret the damping constant and degrees of damping. c-) t = 5s with t = 20s compare the situation in their time. What changes have occurred?
(1) The bar of mass, m= 10kg and length L=lm is fixed at the left end as shown below. Find; (a) The equations of motion of the system, k=2000N/m, k= 1000 N-m/rad. (b) The natural frequencies of the system (c) The response of the system if initial displacements are 01(0) =5rad and 0 2(0) = -5rad k, k k 30 kg Figure 1: spring - mass system
Question 3: [24] Crack AB of a slider crack mechanism shown in Figure 2 rotate at a constant speed of 300 rpm in clockwise direction. The connecting rod BC has a length of 1 m and incline at 45° to vertically positioned piston C. B 1 m |0.2 m 45 Figure 2: Slider crank mechanism 3.1. Draw the displacement diagram of the mechanism shown in Figure 2 to scale. (4) 3.2. Use a vector diagram to determine the velocity of the piston C and connecting (8) rod BC. 3.3. Calculate the acceleration of piston C and the angular acceleration of (12) connecting rod BC.
A body of mass 100 kKg is suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.
For given mass (m=10kg) and two springs systems k1=30 N/m and k2= 20N/m. Find the following 1. Circular Frequency and natural frequency 2. If initial displacement is 50 mm and initial velocity is 0, what is max displacement and max velocity. 3