8. Determine the natural frequencies of the system shown in Fig 1, where fi (t) =...
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...
Determine the natural frequencies and vibration modes of the two degree of freedom rectilinear system shown in the following figure. please detail all the steps ans: k m, ww m2 DCL LEE LFF Оn1 — 0 k(m1+m2) Wn2 7ш.Тш X1 X2 -т, — Х, ( X2 X1 т2
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
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...
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...
Determine the natural frequencies of the two-degree-of-freedom mechanical system of Figure P6.37 6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. N N 2 x 10 3 x 10 10 2 kg 3 kg FIG. P6.37
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
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...
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
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,...