22–17. The 15-kg block is suspended from two springshaving a different stiffness and arranged a) parallel to eachother, and b) as a series. If the natural periods of oscillationof the parallel system and series system are observed to be0.5 s and 1.5 s, respectively, determine the spring stiffnesseski and k2.00000

Answered: Image /qna-images/answer/c8e61655-eada-453c-813c-6de0e05e1a53.jpg

Answered: 22–17. The 15-kg block is suspended…

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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A mass weighing 4 pounds is attached to a spring whose constant is 2 ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equlibrium position with a downward velacity of 12 t/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g -32 /s for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in t) of the mass at this instant? ft
A spring extends by 5 centimeters when loaded vertically with 2.5kg of weight. A new weight of 1.75kg was attached to it and was displaced 6cm from its new equilibrium position and was released from rest. Determine the frequency of vibration in rad per second?
A weight attached to a spring of stiffness 3.0 lb/in has a viscous damping device. When the weight is displaced and released, the period of vibration is found to be 1.80 seconds and the ratio of consecutive amplitudes is 4.2 to 1.0. Determine the amplitude and phase angle when a force F-2cos(3t) acts on the system.
The spring constant of the spring-mass-damper system is k = 5 kN/m, the damping constantcritical value ckr = 200 Ns/m and logarithmic decrement δ = 2. System initial conditionsare x0 = 0 m and v0 = 1 m/s. Determine the damping due to the initial conditionsthe maximum value xmax of the displacement of the characteristic vibration and its moment of occurrence tmax. Specifyresponse, i.e. in this case the values of the variables needed by the station x(t).
A damped spring – mass system has a mass of 2 kg, a spring of stiffness 98 N/m and a dashpot with a viscous damping coefficient of 42 Ns/m. If the mass is disturbed by 70 mm and then released from rest, determine the displacement of the mass after 0·12 seconds
An electric motor and its base have a combined mass of M = 12 kg. Each of the four springs attached to the base has a stiffness k =480 kN/m and a viscous damping coefficient c. The unbalance of the motor is equivalent to a mass m =0.005 kg located at the distance e=90mm from the center of the shaft.When the motor is running at ω = 400 rad/s, its steady-state amplitude is 1.8 mm.Determine (a) the damping coefficient of each spring; and (b) the phase anglebetween the displacement of the motor and ωt.
The ratio of successive maximum amplitudes for a particular spring-mass system for which K = 100 N/m and M = 4 kg is found to be 0.8 when the system undergoes free motion. If a forcing function F = 10 cos 4t is imposed on the system, determine the maximum amplitude of the steady-state motion.

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