27 M%3D X (0) %3D (0) = 3.
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- Consider the following for a single-degree-of-freedom system with m = 1. X, k = 2.5, and c = 1.8. Here, the value of X indicating of the number of your Q1 (a) group. For example, if your group number is 15 gives X = 15, therefore the values of m = 1.15. If your group number is 9 gives X = 9, therefore the values of m = 1.9 Find; Natural frequency, Wn (ii) Linear frequency, fn (iii) Critical damping constant, c. (iv) Damping ratio, 3 (v) Damped frequency, WaCalculate the solution of the two-degree of freedom systemm given by: [27 -3 = 1 K = , 1 x0) = %3D %3D of tion X (0) = cosv2t+ cos2t cosv2t- cos2t cosv2t+ cos2t cosvZt+ cos2t sinvZ t+ cos2t sinv2t+ cos2t O cosv2t+ cos2t cosv2 t- cos2t 3/2Exercise 3. Calculate the solution of the following system: 1 27 -3 *(t) + -3 x(0) = 3 3 ; x(0) = 1 1
- 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=0.05mUse the graphical method to find the optimal solution for the following LP equations: Min Z=10 X1 + 25 X2 Subject to X1220, X2 ≤40 ,XI +X2 ≥ 50 X1, X2 ≥ 0.Find the ditferential equation from the transfer of the function for the Giving following system and draw the block diagram of the system. x(s) H(s) u(s) 0.5s + 1
- 4G I. 3:22 A moodle1.du.edu.om Consider the 3 degree of freedom robot manipulator as shown in the figure Link 3 Länk 2 Trint 1 The objective is to find the kinematics inverse of the robot Px=0.9 m, Py=0.6, L1=1.5m, L2=1.5m and qz= 2 rad The value of cos(q2) is equal to Choose... + The positive value of sin(q2) is equal to Choose... + The value of q2 in rad is Choose... + The value of qı in rad is Choose... + The value of q3 in rad is Choose... +Given the following eavation for a mass-spring it of too muy MX + CX + KX = KYS кута where we N assume ratives to tosHS ON 20H ( a) the system is massless tho KINO bluan (6 the spring has an initial displacement of Y = 10 in c) the spring constant eavals 5 16/in d) the damping coefficient eavals 0₁1 (16-5/in) HOES & HATTnon homogeneous system using the Laplace transform
- Draw by hand the Bode plot of the following systems. 1. 50 G(s) : s(s² + 4s + 8) 2. 20(s + 1) s(s² + 2s + 10)(s + 5) G(s) =/Simulate to solve the following ordinary differential equation by using Simulink tool box and represent the output result. x(t)= sin(3t) = 3x(t) + 1-2y dtQ1: Find the Laplace inverse for the function 8 3 F(s) = 3 s2 + 12 s2 – 49 Q2: Solve IVP y" – 10y' + 9y = 5t ,y(0) = -1 and y'(0) = 2 %3D %3D