Q3The landing gear of an airplane has m = 2000 kg.It can be idealized as the spring-mass-dampersystem shown in the figure. If the runway surfaceis described y(t) = 0.2 cos 157t, determine thevalues of k and c that limit the amplitude ofvibration of the airplane (x) to 0.1 m.y(t)x(t)mRunway

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Answered: Q3 The landing gear of an airplane has…

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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Magnitude of 23N harmonic force is acting on an undamped system with mass of 10kg and stiffness of 1000N/m. The harmonic force frequency is twice the system natural frequency, and initial condition given by Xo=0 and v₁= 0.2m/s. Obtain the equation of motion for the system. 3 Fcoset X
Q2\ Amass is suspended from a spring system as shown in fig. Determine the natural frequency of the system. Given: m=30kg K1 = 1000 N/m K,= 2000 K3 =4000 N/m Q3\ the mass of a spring-mass-dashpot system is given an initial velocity 10W„ . where 10W,is the undamped natural frequency of the system. Find the equation of motion for the system, when F = 0.5. Q4\Find the natural frequency of the system shown in fig. Given: m=10 kg, K, = 2500 , K, = 1500 N/m K3= 2000 N/m- ttt A(m)
Q4 The landing gear of an airplane has m = 2000 kg. It x(1) can be idealized as the spring-mass-damper system shown in the figure. If the runway surface is described y(t) = 0.2 cos 157t, determine the y(1) Runway values of k and c that limit the amplitude of vibration of the airplane (x) to 0.1 m.
An electric motor with a mass of 20 kg is placed in the middle of a beam that is jointly connected on both sides. Rotor its unbalance is equivalent to a mass of 0.3 kg at a distance of 0.020 m from the axis of rotation. Due to the electric motor force acting on the beam t Sin F F  0 . The rotor is rotating at an angular speed of  = 40 rad / sec. Engine under the influence of force Find the displacement amplitude at the point where it is located (in the middle). The beam mass will be neglected. The beam has a modulus of elasticity E = 200000000000 N / m2 (200 GPa).
A mass m = 4 kg is attached to both a spring with spring constant k = 577 N/m and a dash-pot with damping constant c=4N-5/m. The mass is started in motion with initial position za = 1 m and initial velocity ty - 3 m/s. Determine the position function z(t) in meters. F(t) = e^(-5t)cos(12t)+1/6e^(-5t)sin(121) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can bo written in the form z(t) - Ciecos(wit - a1). Determine C, wi aand p. C = (assume 0Saj < 2n) Graph the function z(t) together with the "amplitude envelope" curves a= -Cie and z= Cie. Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c= 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t) = Cocos(wot – an). Determine Co, ab and ao. Co = (assume 0< ao < 2n) Finally, graph both function r(t) and u(t) in the same window to…
An automobile suspension system is critically damped, and its period of free oscillation with no damping is 1 s. If the system is initially displaced by an amount and released with zero initial velocity (at t = 0; x(0) =x, and v(0) = 0) %3D a- Determine the value of the angular frequency of free oscillation with no damping. (w. = ??) b- Deduce the value of friction factor (g =??) с- Write the expression of position as a function of time of the system, if the system is critically damped. (x(1) = ??) d- Deduce the expression of the velocity of the system. (v(t) = ??) %3D
Identify the expression for the natural frequency of the system shown in the figure.
Consider a vibrometer composed of a mass of m = 3.86 kg suspended from a spring of elastic constant k = 50 kg/m inside a box as shown in the figure. If placed above a machine that produces a vertical motion x(t) = 0.09sen3t m. Find the equation of motion of the system and the absolute amplitude of the mass in its steady state.
In vibration testing, an instrumented hammer is often used to hit a device to excite it and to measure the impact force simultaneously. If the device being tested is a single- degree-of-freedom system, determine the response at t = 0.55 s of the device considering: M = 1 kg, c = 5 kg/s, k = 100 N/m, and F(t) = 0.35 (t) +0.28 (t - 0.5) N Assume that the initial conditions are zero. 0.08 mm 0.98 mm 1.77 mm 3.29 mm 2.08 mm Test Structure. FO C www. Impact Hammer ▼x(1) D
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Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT: mechanical vibrations)
2 – Response of the two-degree-of-freedom system shown in to an initial displacements of uj 0.915 and u2 = 2.0 is such that q2 = 0. Find the mode shapes and a, where ki = a k2. Normalize each mode so that the modal mass has unit value. Write the equation for the force in the springs. k, 8m kz 2m U2 ui

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