4. Consider the system below such that z1 and z2 are zero when the springs are relaxed.4.a Draw the free body diagrams and derive the equation of motion.4.b Consider the case F(t) = 0. Derive the natural frequencies and construct the (homogenous) solution of thesystems.4.c Consider the case F(t) = Fo sin(@t). Derive the particular solution of the system.4.d Consider the numbers m = 1 [kg], k = 1 [N/m], Fo = 1 [N] and plot the amplitude and the phase of steadystate oscillations as functions of the excitation frequency o.FeeeeeemLeeleeeeeeeceee

1. Two Masses-Two Springs system of vibration 2. All spring constants are equal i.e., k1 = k2 = k3 =…

Answered: 4.a Draw the free body diagrams and…

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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Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses moveto the right direction;a.Construct the free body diagram and develop the equation of motion for each mass.b.Write the equation of motion for the system in matrix form such that it is completewith all parameter values.c.Estimate the natural frequencies of the system where the spring coefficient, k1 = k2= k3 = k4 = 127 N/m and the masses, m1 = m2 = m3 = 17 kg.d.Determine the mode shapes of the system. Assume x1=1 in modal vectorNote: No need to sketch the mode shape diagram
2) If the under-damped spring mass system shown at right is CON subject to the force F(t)= Fe (is the radial frequency of excitation), find the steady-state response of the system by the method of Laplace transformation. k2 m FO k/2
2. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t)=C₁e Pt cos (@₁t-a₁). Also, find the undamped position function u(t)= Cocos (@ot-ao) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m = 2, c = 4, k = 6, x₁ = 4, V₁ = 0 x(t) = which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or…
pivoted at point P. A mass m is attached to one end of the rod, while two identical springs are attached to the other end of the rod. The displacement x is measured from the equilibrium position. Assuming that x is small, find the equation of motion and the natural frequency of the system using the energy method. 2. In the system shown in Figure 2, the massless rigid rod of length l = 4 + l2 is k P m. k Figure 2
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e -p' cos (@,t-a,). Also, find the undamped position function u(t) = Co cos (@ot – ao) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c=0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). c= 4, k = 6, xo =3, vo = 0 m =
Q2: For a system the equations of motion are as shown below, find frequencies and mode shapes. Т Ţ X₂(1) muqu k, = k m₁ = m k₂= nk m₂ = m k₁ = k
Find the natural response of the following spring–mass system with m=1,k= 1 and the initial position and velocity being both equal to 1. Please answer in typing format please
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position x and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, runderdamped. If it is underdamped, write the position function in the form x(t) =C₁ e Pl cos (@t-α₁). Also, find the undamped position function u(t) = Cocos (ot) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). m = 16, c=40, k = 169, x = 5, Vo = 16 x(t)=, which means the system is (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.)
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e - pt cos (0,t-a,). Also, find the undamped position function u(t) = Co cos (@ot - a0) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c= 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m = - 4' c= 3, k= 8, xo =7, vo = 0 x(t) = which means the system is (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to and ess than or…
1. For the mechanical system shown, A. Obtain the differential equations and set them in the matrix form. 2m B. find the natural frequencies and related amplitude ratios as functions of m and k. C. For m = 4 Kg, k = 100 N/m, x,(0) = 1, x,(0) = 1, 1 (0) = 0, X2(0) =0, find x, (t) and x2 (t) in normal and general vibrations. 1. For the mechanical system shown, A. Obtain the differential equations and set them in the matrix form. 2m B. find the natural frequencies and related amplitude ratios as functions of m and k. C. For m 4 Kg, k= 100 N/m, x,(0) 1, X2(0) 1, 1 (0) 0, *2(0) 0, find x (t) and x2 (t) in normal and general vibrations E WW
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e - pt cos (0,t-a,). Also, find the undamped position function u(t) = Co cos (@ot - ao) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c= 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). C = 1 m = - 4 c= 3, k= 8, x, = 7, vo = 0 x(t) = 14 e -4t - 7 e -8t , which means the system is overdamped. (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater…
Derive the equation of motion in terms of the variable x for the mass-spring-damper system shown in Figure 5 Find the eigenfrequency f in Hz and the logarithmic decrement o for m = 100kg k= 25-10 and c= 120- N.s m m Neglect the mass of the crank AB and assume small oscillations about the equilibrium position shown. A a B

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