5. Consider the system below with m1 10 kg, m2-20 kg, b 20 N-s/m, k- 60...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
Find the state space representation of the following system. Show all work. m2 • m1 = 3 kg • m2 = 1 kg kı = 4 N/m k2 = 1 N/m C1 = 2 Ns/m C2 = 5 Ns/m C3 = 3 Ns/m
Problem 8: A simplified model of a glider is where y is the flight path angle in radians, v is the airspeed in m/sec, n -L/mg is the load factor, L is the lift in Newtons, m is the mass in kg, and k 61.6594 and k 4.8747x103 are constants for the glider. (a) Given that y -0.15 rad, and the airspeed is 50.8691 m/sec, find the necessary load factor to maintain equilibriunm (b) Let the state vector be [7...
m1 m2 Figure 1: 2dof 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices Note that setting k30 in your solution should result in the stiffness matrix given by Eq. (4.9). a. Calculate the characteristic equation from problem 4.1 for the case m1-9 kg m2-1 kg ki-24 N/m 2 3 N/m k 3 N/m and solve for the system's natural frequencies. b. Calculate the eigenvectors u1 and u2. c. Calculate 띠(t) and...
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2...
Need Matlab for part d)
3. The following questions relate the figure below of 2 couple spring-mass systems T2 fint) (a) Derive the 2 differential equations (one for each mass) of this system (b) Now derive the Transfer-Function from fin → Xi (c) Now derive the state-space representation (A,B,C,D) of this system. Hint: There should be 4 states (position and velocity of each mass). The output of this system is still y (which will probably be the first state in...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
Consider the system shown in the figure right, where two blocks m1=5 kg, and m2=10 kg are connected to each other by a string that passes through a massless pulley. The stiffness constant of the spring attached to m1 and the wall is k=120N/m and the coefficient of kinetic friction between m1 and the surface is given to be μk=0.2. If the system is released from rest when the spring is at its equilibrium length and m2 is at a...
Consider the diagram below where m1 = 10 kg, m2 = 5 kg and m3 =
10 kg. (a) Find the force if the acceleration of all boxes to the
left is 10 m s−2 . (b) Find the forces between each box F12, F23,
F21, and F32.
M13 1721 m2