1. For the mechanical system shown, A. Obtain the differential equations and set them in the...
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations, in terms of velocity, to represent the system, where k is spring Constant, m is the mass and b is damper. (Hint: draw two Free Body Diagrams and obtain two equations in terms of x1 and x2 only). X1 - Ft mi m2 M TTTTTTTTYYTTTTTTTTTYYTTTTTTT Fig 1.1 b) What components and energy source do you need to use in order to build an electric...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x (0) 0, x, (0) 0.001 m 2k E 2m Figure 4 Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2E 2m 1n Figure 4 Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
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...
with steps please 04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2kE TIITTTUITTU Figure 4 04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural...
(t) 8k mm sm For the vibratory system shown in the figure, k=15000 N/m and m=1.5 kg. a. Derive the equations of motion. b. Calculate the natural frequencies. c. Find the ratio of the mode amplitudes and draw the mode shapes. Xy(t) w 3k 2m TA X2(t)
I need your help 1. Answer the following questions for the system below. (60 pts) (a) Derive the equation of motion in a matrix form: [m]{x}+[k]{x}={F(t)} (b) Write the characteristic equation. (c) Find the natural frequencies and natural modes. (d) Prove the orthogonality of the natural modes. (e) Determine the amplitude of x, at t=1 sec when it starts to vibrate from rest at t=0 sec. X2 4k 2k 4m m cos 100
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 (-?
mechanical vibration A mechanical system is governed by the two equations below. What are 1. the natural frequencies () and eigenvectors (u(t)) of the system? by-step workings to get full credit. Show step- 120]