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Please help! QUESTION 1 Consider a freedom model that can be used to study the vibratory motion of a coupled rectangular vibration system shown in Figure Q1. The two uniform rigid bars are of equal length but have different masses. Figure Q1 Use the Lagrange method to establish the differential equation of motion for the system using the following formula: (10) Assuming the solution of the differential equation is of the form: W(t) = Acos(wt) + Bsin(wt) Find the natural frequencies (w) and develop the state-space model. Also, find the stiffness matrix (K) and the mass matrix (M) obtained from the equation given by: 0.36 50.884 50.884 Determine: - The normalized stiffness (K) - The natural frequencies (w) of the system in Hz for the value considered above: 1.6 - Its eigenvalues and eigenvectors - The modal mass matrix (M) with the diagonalized matrix A [40 marks] QUESTION 2 Consider the system shown in Figure Q2 for the case where kg = m2 = 240 N/m. Write the equations of motion in vector form and compute each of the following: (a) Natural frequencies (b) Mode shapes (c) Eigenvalues (d) Eigenvectors Show that the mode shapes are orthogonal and show that the eigenvectors are orthogonal. Also, show that the mode shapes and eigenvectors are related by M. Figure Q2

          Please help!

QUESTION 1
Consider a freedom model that can be used to study the vibratory motion of a coupled rectangular vibration system shown in Figure Q1. The two uniform rigid bars are of equal length but have different masses.

Figure Q1

Use the Lagrange method to establish the differential equation of motion for the system using the following formula:

(10)

Assuming the solution of the differential equation is of the form:

W(t) = Acos(wt) + Bsin(wt)

Find the natural frequencies (w) and develop the state-space model. Also, find the stiffness matrix (K) and the mass matrix (M) obtained from the equation given by:

0.36
50.884 50.884

Determine:
- The normalized stiffness (K)
- The natural frequencies (w) of the system in Hz for the value considered above: 1.6
- Its eigenvalues and eigenvectors
- The modal mass matrix (M) with the diagonalized matrix A

[40 marks]

QUESTION 2
Consider the system shown in Figure Q2 for the case where kg = m2 = 240 N/m. Write the equations of motion in vector form and compute each of the following:
(a) Natural frequencies
(b) Mode shapes
(c) Eigenvalues
(d) Eigenvectors

Show that the mode shapes are orthogonal and show that the eigenvectors are orthogonal. Also, show that the mode shapes and eigenvectors are related by M.

Figure Q2

please help question consider dene freedom model tha hcen usco sudy the vibratony motlon 0 coupled rectangular vibration system shown figure qi tle two uniform rgid bars are yural length but 61625

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