How many DoF does the following system have assuming plane motion (2D problem)? How many non-zero...
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
2. Assuming for a 2-DOF system the following eq uations of motion, andg so kip, g 386.4 in/s, k1 100 kip/in, Pi(t) 10 kip. P2(t) a. The two natural frequencies of the system. (25%) b. The two eigenvectors normalized with respect to mass and the 10 kip, determine the following: corresponding checks. (25%) c. Assuming a modal damping ratio ξ equal to 0.02, express numerically (as b, and N10) the uncoupled two equations of motion as shown below assuming classical...
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m OX -M29 2 m29 0 mal -29 Where m=m2 Em g -gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response (0) (0)) Note: xi(t) = XO, xa(t) = 0 and 1) = xo.* () = 0 d) If the system is excited by a harmonic force F. (t) =F, sinot,...
Problem 2) For a 2 DOF system the equations of motion are given as: [mi 0 0 m2 (X2 mig L -m29 L -m29 L m29 L Where m1 =m2 =m g=gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response fX:(0) Note: x1(t) = xo , x2(t) = 0 and xi(t) = xo , iz(t) = 0 d) If the system is excited by a harmonic...
Problem 4. (20 points.) How many poles does the following system have on the right-half plane!? H(s) ยูโ-2s4 +283 +482 + 11s+10
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www Problem 5 (20%) For the system shown in Figure...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww- For the system shown in Figure 5, a. How many degrees of freedom...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2 For the system shown in Figure...
1. A non-empty heap has n nodes. How many interior modes does it have? 2. A non-empty tree has n > 1 nodes. How many of them are interior nodes? 3. A non-empty heap has L leaves. How many nodes does it have?
For the problem: A) how many degrees of freedom does the system have? B) sketch a free-body diagram for each rigid body in the system. C) Write Newton’s second law of moments for each rigid body. D) List the unknowns, and compare to the number of equations. If necessary specify any kinematic constraints that are required to provide enough equations to determine the unknowns. 2.24 A mechanical system containing translating and rotating components is shown below. The left end of...