Answer Happy

20)+(288 1:0)=10 A simplified vibration model for the propeller blade of a light airplane is represented as the equation below: 3.75 0 28500 -180001 [xt) 0 5.50)|xz -18000 14000 1x2 The dynamic matrix of the system is D=7600 - 4800 -3600 2800 The natural frequencies of the system are w; = 100.0 (rad/s) and W2 = 20.0 (rad/s). (a) Explain the normal mode shape for each natural frequency; (b) Determine the principal coordinates in terms of the generalized coordinates: (c) Determine the equation of motion with respect to the principal coordinates (d) If the initial conditions for the vibration are 6:00-10:5] m) and (30)=180] (ms) Determine the initial conditions with respect to the principal coordinates: (e) Determine the free vibration of the system with respect the principal coordinates in response to the initial conditions listed in (d).