4.4. A spring-mass system is subjected to a harmonic force which has an amplitude30N and frequency 20 rad/s. The system has mass m = 5 kg, and stiffnesscoefficient k= 2 x 10° N/m. The initial conditions are such that xo = 0, io =2 m/s. Determine the displacement, velocity, and acceleration of the mass after0.5, 1, 1.5 s.

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Answered: 4.4. A spring-mass system is subjected…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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рис Q2. A railroad bumper (which it is used to stop the railroad car) is designed as a spring in parallel with viscous damping. What is the bumper's damping coefficient such that the system has a damping ration of 1.25 when the bumper is engaged by 20,000 kg railroad car and has a stiffness of 2×10 N/m. The railroad car is traveling at initial speed of 20 m/s when it engages the bumper. What is the time at the maximum deflection occurs when dx/dt=0. brings each
Q2/ The measurements on a mechanical vibrating system show that it has a mass of 8 kg and that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the vibrating system has a dishpot attached which exerts a force of 40 N when the mass has a velocity of 1 m/s, find (1) critical damping coefficient, (2) damping factor, (3) logarithmic decrement, and (4) ratio of two consecutive amplitudes.
PART OF MECHANICAL VIBRATIONS A viscously damped single degree of freedom mass–spring system hasm = 0.5 kg, k = 1000 N/m, and c = 10 N ·s/m. The mass is set in motion withinitial conditions x0 = 0.05 m and x˙0 = 0.5 m/s. Determine the displacement,velocity, and acceleration of the mass after 0.3 s
A block of mass m = 5 kg is attached to a spring of spring constant k. The block oscillates in simple harmonic motion on a frictionless horizontal surface. The block-spring total mechanical energy is 36.1 J. The maximum velocity of the block, vmax, is:
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An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are w rad/ s and T s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are m
P3. The peak amplitude of a mass-spring-damper system, under a harmonic excitation, is observed to be 1 cm. The undamped natural frequency of the system is 5 Hz, and the static deflection of the mass under the maximum force is 0.5 cm. Now, instead of a harmonic excitation, a sudden impulse of 10 N.s is applied. Determine the response of the system. 4 z 0.5 cm
4.3. In a single degree of freedom undamped spring-mass system, the mass m = 3 kg, and the stiffness coefficient k = 2 x 103 N/m. The system is subjected to a harmonic forcing function which has an amplitude 60 N and frequency 30 rad/s. The initial conditions are such that xn = 0.0m and io = 1 m/s. Determine the displacement, velocity, and acceleration of the mass after t = 1 s.
Consider the two degrees of freedom mass spring system below. Assume M = 10 kg, m = 3 kg, K1 = 100 N/m, K2 = 150 N/m, K3 = 867 N/m and K4 = 380 N/m. %D The ratio of the second natural frequency to the first one, i.e. w2/w is X1 K2 www X2 K4 K1 M K3 m Frictionless surface 3.30 4.13 2.74 0.30 5.38 Activate Windows
Q.4 A damped single degree of freedom mass-spring system is excited at resonance by a harmonic forcing function which has an amplitude of 40 N. The system has mass m of 3 kg, a stiffness coefficient k of 2700 N/m, and a damping coefficient c of 20 N·s/m. If the initial conditions are such that xo = 5 cm, and xo = 0, determine the displacement, velocity, and acceleration of the mass after t = 0.2 s.

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