Find the response X1(t) , X2(t)
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Find the response X1(t) , X2(t)
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- :) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2kQ2: Find the steady- state response of the system in Fig. below for the following data: kı=1000N/m, k=500N/m, c=500N.s/m, m=10kg, r=5cm, Jo=1kg.m², Fo=50N and 0=20rad/s Pulley, mass moment of inertia Jo k2 Fo sin wt m x(1) kxa 0- 1 point) Which of the systems presented on Fig. 2 is stable and which unstable? (a) t Fig. 2. System response (b) A
- In the process of freeze drying, ice goes directly into water vapor. What is the temperature at which this process can take place? Select the correct response: At the triple point of water Above the triple point of water O Any of the above, depending on the pressure Below the triple point of water1. Equation of Motion 2. Find the response of the system, as the initial condition is (X, = 2 cm at the block). %3D Note: m= 1kg, Mlise 3 kg, c=50 N-s/m, k 200 N/m, and r= 10 cm. %3D and determine the response after 10 sec. 2r ActivateProblem 1: Laplace Transforms For a spring-mass-damper system with the following characteristics m = 70 k= 707 C = 69 Xo = 0 m/s Vo = 0 m/s If an forcing function F(t) = 100tet N is applied to the box at t = 0s, find x(t) for the system analytically. HINT: I STRONGLY suggest that you use the Laplace transform method. Please box your final x(t), and plot your solution.
- 1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.1 - Explain Van-Neumann stability by finite difference schemes for this equations a- Laplace equation. J²u dyz (x, y) = 0 J²u dx2(x, y) + b- poison equation. J²u J²u { (x, y) + əy² (x, y) = f (x, y) əx²Q₁ / uniform string stretched between the points (0,0) and (0) is given the following intial displacement and Intial velocity. y (x,0) = sin x ORXKL orxst y (x,0) = 1 45x52 35x5L find the displacement response y(x, A)?
- 4. A model for an airplane's pitch loop is shown below. Find the range of K that will keep the system stable. Can the system every be unstable for positive values of K? Commanded pitch angle + Controller K(s + 1) (s + 4.85) 1 Aircraft dynamics s + 10 s² +0.6s +9 Gyro Pitch angleMultiple DOF SystemsA 2-D spring-mass, frictionless system has the following parameters:m1 = 72m2 = 27k1 = 381k2 = 183x1,0 = 0 mx2,0 = 1 mv1,0 = -1 m/sv2,0 = 0 m/s In MATLAB, solve numerically for x1(t) and x2(t).MA Figure (2) 3- The time response of a liner spring-mass-damper system with the mass of (m), the stiffness coefficient of (k), and a dampirg constant of (c) is given below in figure (2) with a set of coordinates marked by fillec circles. x(t) is in meters, it is in seconds. Indicate the units of all quantities involved in your solutions when calculate 0 -1- (0.53, 1.78) (0,0.8) 2 (2.1,-1.3) (3.7,0.9) L 4 (5.3,-0.7) - The damping ratio of the system. Its natural frequency w., damping corstart c, and stiffness coefficient k; for (m-1.25 kg). III- The amplitude of the motion if the phase angle is given as (0.4 rad). IV. Its initial conditions. (6.86, 0.5) 10 t[sec]