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/...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1 MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
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...
Q2. A mechanical system is shown as Figure 2, where external force uz is the input and displacement y2 is the output. The force acting on m2 has a linear relationship with uj as u2=Aui. 1) List system equations; 2) Draw block diagram of the control system; 3) Build the block diagram in Simulink (screenshot and paste your diagram in your submission). ki U1 mi k2 Yi Y bi U2 V m2 y2 Figure 2
5. Consider the system below with m1 10 kg, m2-20 kg, b 20 N-s/m, k- 60 N/m and fas a step input of 10 N (a) Derive the transfer function of the system between fand z2. (b) Derive a state space representation of the system. (c) Use MATLAB to plot the output (z2 - z1) and (z2' - z1') m2
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
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...
2. For the system shown below, where ki k2-120 N/m, k 150 N/m mi-3kg, m2-5kg and m3-9kg: F(O) k ny nt1 12 Point 3 Point 1Point 2 Find the mass and stiffness influence coefficients.
Problem 2 Determine the transfer function 01(s)/M(s) for the shaft-gear mechanical system in the figure, where 1(s) and Ms) are the Laplace transforms of the angle 01(t) and of the moment m(t). Use the time-domain mathematical model of this system. Known are J1, ki, J2, c, k2, Ni and N2. N. 1000 0,m 0 000 N Problem 3 By using the transfer function 1(s)/Ms), determined in Problem 2, calculate and plot 01(t) using the step input command of MATLAB. Known...
mwu Q3. a) Consider the mechanical system shown, obtain the transfer function x(s)/P(s), assuming all initial conditions are zeros. (10 marks) Ž p3k, у b) For the question in part (a), assuming that m = 20 kg, b2 = 12 N.s/m, K1 = 20 N/m, K2 = 35 N/m and P=1 N. Write a MATLAB program to produce the response curve x(t). (15 Marks)
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...