A mass, m of 20 kg consider one vertical motion only with angular displacement, 0 =wt, with spring coefficient, k of 1 6 kN/m as shown in Figure Q1. If the systemoscillates at free motion yY sin(@nt) with amplitude, Y of18 mm:%3D(i)Determine the natural frequency of the system, @n.(ii)Solve the time taken to complete one cycle of motion....(111)Analyze the velocity of the mass, y at position A. A mass, m of 20 kg consider one vertical motion only with angular displacement, 0 =wt, with spring coefficient, k of 1 6 kN/m as shown in Figure Q1. If the systemoscillates at free motion y= Y sin(wnt) with amplitude, Y of 18 mm:AymYY - 40 =otFigure Q1-------Bwww

Answered: Image /qna-images/answer/4d5c1e93-8f45-4c2b-a2c4-1eabd5f44135.jpg

A mass, m of 20 kg consider one vertical motion only with angular displacement, 0 = wt, with spring coefficient, k of 1 6 kN/m as shown in Figure Q1. If the system oscillates at free motion y = Y sin(@nt) with amplitude, Y of 18 mm: (i) Determine the natural frequency of the system, @n. Solve the time taken to complete one cycle of motion. (iii) Analyze the velocity of the mass, ý at position A.

A mass, m of 20 kg consider one vertical motion only with angular displacement, 0 = wt, with spring coefficient, k of 1 6 kN/m as shown in Figure Q1. If the system oscillates at free motion y = Y sin(@nt) with amplitude, Y of 18 mm: (i) Determine the natural frequency of the system, @n. Solve the time taken to complete one cycle of motion. (iii) Analyze the velocity of the mass, ý at position A.

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

A 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with damping constant c = object is initially displaced 5 m above equilibrium and released. Find its displacement and time-varying amplitude for t > 0. 7 N-sec/m. The y(t) e-0.184t (5 cos (0.9t) + sin(0.9t)) The motion in this example is O critically damped O overdamped O underdamped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) 4 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? 0.977 What is the maximum possible amplitude? 2.30
For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and equivalent damping coefficient when x (the displacement of the 2 kg block) is used as the generalized coordinate. b- Derive the equation of motion of the system in terms of equivalent system parameters (equivalent mass, equivalent spring stiffness and equivalent damping coefficient). 3000 N/m 2 kg 200 N.s/m /=0.04 kg-m² r = 10 cm 1000 N/m 1 kg I' 400 N.s/m ial
3. Consider the single degree of freedom spring-mass system shown in Fig. where k = 4 x 10$ N/m and m = 8 kg. It is being excited by a harmonic forcing function, F1e'o", at a frequency, wf. (a) If the excitation frequency is 200 rad/s, design a dynamic absorber to eliminate the vibration at coordinate x]. The only available spring for use in the absorber is identical to the one already used in the system. (b) If the 4x10° N/m absorber spring is used in conjunction with a 2 kg absorber mass, at what forced excitation frequency (in rad/s) will the steady-state vibration of coordinate x1 be eliminated? k m
A 2 DOF mass-spring system shown below with n = 1, k = 8, and m initial conditions 2₁ (0) = 1, 2₂(0) = 0, ₁ (0) = 0, and ₂(0) = 1. (a) Find the natural frequencies and normalized modal matrix [X] for the system. T x₁ (1) (b) Using modal analysis and the Cartesian solution form, find the free vibration re- sponse of the system x₁(t) and x2(t). Ţ x2₂ (1) www. 00000 = m m₁ = 00000 k₁ = k 00000 k₂ = nk m₂ = m k3= k = 2 DOF mass-spring system. 2 with the
t. Design the following application case The mechanical vibration system is shown in Figure (a). When a step input with 3N amplitude is subjected to this system, the movement rule of the mass m is shown in Figure (b). Evaluate the values of mass m, damping constant c and spring constant k. m (a) F-3N XX 1.0 x(1)(cm) 0 2 (b) M,-0.095 Ⓒ
3
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s
Q3/ For the system shown in figure if the damping ratio is 0.3 derive the equation of motion using Newton's second law and find: a- The natural frequency. b- The damping constant. c- The ratio of any consecutive cycles. k=2 x 10 N/m m = 4.2 kg 10 cm 40 cm 60 cm ITTTI
A mass, m of 20 kg consider one vertical motion only with angular displacement, 0 = wt, with spring coefficient, k of 13 kN/m as shown in Figure Q1. If the system oscillates at free motion y = Y sin(@nt) with amplitude, Y of 13 mm: (a) (i) Determine the natural frequency of the system, o,. (ii) Solve the time taken to complete one cycle of motion. (iii) Analyze the velocity of the mass, ý at position A.
damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…
Consider a two-degrees-of-treedom system shown below What is the amplitude of vibration of mass 2 at the input frequency? (Thi is just ancther way of asking ampitude of the particular solution. The anower must be positive. Use scientific notation with 3 significant figures. Omit units Use mt -3 kg m2 -1 kg k1- 112 N/m - 148 N/m K3 = 155 N/m F1 = 349 cos(o.90 N F2 =0.
A 128 pound object is suspended from a spring with spring coefficient 1 lb/ft. The whole system is suspended in a viscous liquid that has a damping coefficient of 1 lb*sec/ft and subjected to an external force F(t) = 203 sin(5t) + 89 cos(5t). Find a formula describing only the forced response of the object. Use only a single cosine in your answer. What is the formula for the forced response of the object? U(t) = help (formulas)