Decouple the following equation of motion into two decoupled equations of motion. That is, find r (t). 4 [ 11 ] * (t) + +[ 4 -2 -2 2 ] x (t) = 0

Find the inverse Laplace transforms using the table. 10s s2+100 3s s2+7s

6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support

3. Consider the vibrating system described below (t) 4 -2 -2 1 [ói]x+ [ $ ? ]x= 11 * 0 Compute the mass - normalized stiffness matrix, the eigenvalues, the normalized eigenvectors, the matrix P, and show that PTP I and PTKP is the diagonal matrix of eigenvalues A.