Consider a simple model of an airplane wing given in figure below. The wing is approximated as vibrating back and forth in its plane and is massless compared to the missile carriage system (of mass m). The modulus and the moment of inertia of the wing are approximated by E and I, respectively, and / is the length of the wing. The wing is modeled as a simple cantilever for the purpose of estimating the vibration resulting from the release of the missile, which is approximated by the impulse function Fa), Calculate the response and plot your results for the

Consider a simple model of an airplane wing given in figure below. The wing is approximated as vibrating back and forth in its plane and is massless compared to the missile carriage system (of mass m). The modulus and the moment of inertia of the wing are approximated by E and I, respectively, and / is the length of the wing. The wing is modeled as a simple cantilever for the purpose of estimating the vibration resulting from the release of the missile, which is approximated by the impulse function Fa), Calculate the response and plot your results for the

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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6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
For the mechanical system shown below, find the equation of motions and the system matrix. Where (x = X ewt)
Consider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. Pell (P2 R2 P1 Pa ¡P3 R1 P4 L2 Li Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form. b. If you were to consider the input to the system to be the difference between the pressure on 0(s) either side of the piston, write the transfer function for the displacement of the piston: AP(s) Xj = 0 c. Develop the state equations for this system if the state variables are:
Figure shows a mechanical system. The connecting link has moment of inertia J about its pivot point, and rotation angle is positive clockwise. Position of mass m is positive to the right. Both the angular and translational displacements are measured from the equilibrium position where all springs are undeflected. Derive the mathematical model of this system assuming small rotation angle 8. Link, moment. of inertia J L k₁ www m O k₂ www
2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0
(2) Please write out the Equation of Movements of the following system using matrix. (Figure 2) 1 Note: Lagrange's approach is recommended. „P₂(t) ks ww P₁(t) k₁ wwm, www k₂ m₂ k6 www P3(t) k₁ k3 www m3 www Figure 2: N Degree Vibration System
You are requested to design an automotive suspension or shock absorber system. In order to simplify the problem to one dimensional multiple mass-spring-damper system, a quarter vehicle model is used. The system parameters and free-body diagram of such system is shown below. M₁: Automobile body mass M₂: Wheel and suspension mass K₁: Spring constant of suspension system K2: Spring constant of wheel and tire B: Damping constant of shock absorber (a) Obtain the transfer function of X₁ (s) F(s) T₁(s) = = 2500 kg = 320 kg and T₂(s) = = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁ M₂ X₁ (s) - X₂ (S) F(s) in terms of the parameters of mass, damper and elastance (M, B and K). (b) Express the T₁ (s) and T₂ (s) with numerical values. c) Plot the x₁ (t) and x₁ (t) = x₂(t) outputs of this passive suspension system for the input torque f(t) = 2,000 N. fit) K₂ x₂(t) -Tire
In Figure.4, a car wheel balancer device is used to estimate the location/direction and mass value needed to be attached to the wheel in order to statically balance it and prevent vibration during driving. Your role is to calibrate the system measurement by constructing theoretical calculation of a sample wheel and compare it with the results of the computer. The unbalanced wheel can be modelled as in Figure.5 and the four distributed point-mass as in Table.2.
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3. Suppose the model of a vehicle suspension is given below. Write the equation of motion in matrix form (not in State Space form). Calculate the natural frequencies for k₁ k2 10 N/m, m2 = 50kg, and m₁ = 2000kg. -= - - 103 N/m, 1 x1(c) m1 www m1 Car mass k₁ Car spring k1 k₂ Tire stiffness www x2(1) m2 Tire mass м2 k₂ ↑
Three springs with different spring constants are connected as shown below. You are going to use spring elements to simulate this system. Suppose that the spring constants of the first, second and third elements are k1=3,410 N/m, k2=3,160 N/m and k3=3,380 N/m, respectively. Two horizontal forces are applied to the system (as shown) at nodes. 2 and 3. Find the displacement of node 3 and write your answer in mm (millimetre). Hint: Write your answer with 5 decimal places. For example if you calculated the value 1.2345678, then rounding off to 5 decimal places yields 1.23457 and that is the value you need to type in the answer box. U₁=0 (1) F₂ = 2N U₂ = ? F3 = -1N (2) M U3 = ? (3) U4 = 0
Mechanical Vibration Question is image and also written. 1) Using Lagrange's equation derive the equation of motion of the system given below. Gravitational acceleration is taken downwards.