Consider a 3-element axial vibration model of a fixed-fixed bar. Use finite element analysis to determine the first two natural frequencies w1= IV P where a and b are scalars, I is the length of the bar, E is Young's modulus and p is the density. Determine the value of b using 3 decimal places. b HE 11 and w2=

Find the natural frequency (in Hertz) of the system illustrated in the following figure. Consider the length of the rigid bar as 2L, the mass of the rigid bar as m and assume K1=7,873 N/m, K2=8,185 N/m, M=3 kg, m=3 kg, L=0.5 m and g=9.81 m/s2.

t. Design the following application case m is The mechanical vibration system is shown in Figure (a). When a step input with shown in Figure (b). Evaluate the values of mass m, damping constant c and spring constant k. B (a) yu P=2N X(t)/cm4 0.1095 0.1 0 2 (b) 3 4

3. y 1127 L THE FIGURE IS NOT DRAWN TO SCALE. Consider the cross-sectional area in the xy plane. The parameters are h = 40 mm, a = 36 mm and L = 126 mm.

PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) m (2) {2} cm. = cm, v (0) Sec 00000 m k 00000 k x₂ (1) 5k 0000 Figure 3 00000 k x₂ (1) m 00000 k X3 (1)

The 1 degree of freedom underdamped vibration system is subjected to external force as shown in the figure. (1) Finding a steady state response. (2) Induce the frequency at which the maximum displacement occurs in detail and (3) Find the maximum displacement at that time. (4) Plotting the frequency response function and explain its concept.

III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.

In the P branch of the rotational-vibrational spectrum the first possible transition starts from V=0, J=0.  Select one: True False

please be specific and explain will up vote if correct

is my sloution correct ?