Example # 1For the mechanical system shown, a force of 2 lb( step input) is applied to thesystem, the mass oscillates, as shown in fig. determifrom this response curve. The displacement x is measured from the equilibriumpositionm, b, k of the system0.0095 ft0.1ft45(b)

For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates , as shown in fig. determine m, b, k of the system from this response curve. The displacement x is measured from the equilibrium position x(t) 0.0095 ft 0.1 ft 4

For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates , as shown in fig. determine m, b, k of the system from this response curve. The displacement x is measured from the equilibrium position x(t) 0.0095 ft 0.1 ft 4

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

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
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
S=2 U=0 T=0
4.1. A spring-mass undamped single degree of freedom system is subjected to a harmonic forcing function which has an amplitude of 40N and frequency 30 rad/s. The mass of the system is 2 kg and the spring coefficient is 1000 N/m. Find the amplitude of the forced vibration.
3
Q3/ A mass has (1 kg) connected to spring has a stiffens (16 N/m) move in simple harmonic motion with (20 cm) amplitude. Find: a) max Velocity and max Acceleration. b) The Velocity and Acceleration at distance (12 cm) from equilibrium position c) The time required to move the body from (X= 16 cm).
Q1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor steel grating supported at each level. The structure sometimes is subjected to a vertical oscillation movement during rough sea waves given by function of y(t) = Y sin wt . If the steel grating only moves in the vertical direction and is supported by one equivalent spring and damper at each steel grating pole level with stiffness, k; = (300 x 4) N/m, k2= (200 × 4) N/m and k3= (100 × 4) N/m while damping, c= (15 × 8) Ns/m, c2 = (10 × 8) Ns/m and c3 = (5 × 8) Ns/m, respectively, as simplified in Figure Q1. Neglect the effect of gravitational force. (a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces. (b) Determine the equation of motion in a matrix form using Newton's second law, [m]ÿ + [c]ý + [k]y = F. (c) By omitting the damping and external force parameter, deduce and express the general solution in the form of ([k] – w²[m]){Y} = 0. (d)…
4.12. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass sub- jected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected. 1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected. 2. Manipulate the expression for the force so that it is in the form of f =−khMfcos(ωt+φ). Explain the interpretation of the term Mf , which is called the force transmissi- bility. Plot Mf as a function of ω/ωn for various damping ratios to make a plot similar to Figure 4.20.
Mechanical vibrations
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.
Equation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t). %3D a. Find the linearized equation of motion of the system for the motion that it makes around steady state equilibrium point x, under the effect of constant F, force. b. Find the natural frequency and damping ratio of the linearized system. - c. Find the step response of the system ( Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05m
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…