Consider the mass-spring system in Figure 1. For the systemshown in Figure 1, suppose that k₁ = k, k₂ = k3 = 2k, andm₁ = m₂ = m. Obtain the equations of motion in terms ofX₁ and x₂. Assume that x₂ > x₁.X1A. Draw the necessary free-body diagrams and derive thedifferential equations of motion.B. Determine the transfer functions X₂ (s)/F(s). All the initialconditions are assumed to be zero.x2k3k₂m1m2wwwf(t)Figure 1k₁

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Answered: Consider the mass-spring system in…

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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The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…
4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.
+ b 3. A tuning fork is an example of a "resonant system", that is, one that has a low damping ratio. A model of a (half) tuning fork is rod of mass m with air drag modeled as a damper connected approximately at its middle, and a torsional spring at the base of the cantilever. Assume the cantilever rotates back and forth about its pivot by a small angle o. Because other forces are much larger, you can reasonably neglect the effect of gravity in this model. The moment of inertia of a cantilevered beam pinned at one end is equal to ml2, where I is its length. (a) What is the natural frequency of this system if m= 0.1 kg and k = 2548 Nm/rad, and 1 = 0.1 m. Please give the value in rad/s and Hz. (b) Find an upper bound on the damping coefficient b that insures that the damping ratio of the tuning fork is no greater than = 0.01. (c) For this damping ratio, what is the damped natural frequency of the system? (d) For this damping ratio, what is the decay rate (the size of the exponent…
Q2: For mass-spring system shown. The mass is given an initial displacement x(0)= 0.1 m, and released from rest. Find: 1- The position of the mass after 2 seconds. 2- The velocity of the mass after 2 seconds. 3- Plot the response for three cycles and label the result from 1 & 2. 4- What is the period of oscillation? 5- What is the acceleration of mass (m) after 5 second? Į x(t) k=100 N/m m = 4 kg
Find the equivalent spring constant spring constant of the system. Say, k1 = 20 lb/in, k2 = 35 lb/in, k3=18 lb/in,k4 = 50 lb/in, k5 = 45 lb/in
5. In Figure 4, consider the three shafts as massless torsional springs. When 0, = 02 = 0 the springs are at their free lengths. Find the equations of motion with the torque T, as the input. Figure 4. Mechanical system.
Solve the following IVP's for the undamped (b= 0) spring-mass system. Describe, in words, the meaning of the initial conditions. Also, state the period and frequency and describe their meaning in layman's terms. Assume we are using the metric system.
The load elevator in the figure uses a servomotor that generates a torque on the cable of TT-40'+20, where 0 is the angular position of the servomotor. If the load m feels viscous friction associated with the constant B and the cable has a stiffness represented by the constant k. Determine the transfer function of the system that relates the angular position of the servomotor to the height y of the load. k 3 M B
Determine the equivalent torsional spring constant of a spring that will represent the system such that this torsional spring will be located at where the given bar turns. k=5N/m and l=1.5meters (answer in N- m) * 4 = k = k kz = 2k k3 = 3k F x len
please help only need problem 3 for pic solved using whats asked below Do problem 1 using the principle of superposition. Only do the appropriate sketching for this problem. 1. Solve problem 3 of HW 6 using the Duhamel’s Integral Method.
a=2 b=2 Dynamics question solve

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