Question

The figure shown below represents a simplified model of a jet engine mounted to a wing through a mechanism that acts as a spring of stiffness k and has a mass ms. Assume the engine has a moment of inertia J and mass m and that the rotation of the engine (i.e. the vectoring of the engine) is related to the vertical displacement of the engine, x(t), by the radius, ro (i.e. x=ro). Calculate the equation of motion, x(t) of this system as well as its natural frequency. Create a plot that compares the natural frequency of the system versus the percent that the spring mass is of the oscillating mass. Use your plot to comment on when it is no longer appropriate to neglect the mass of the spring in our modeling.

wing through a mass ms. Assume the engine has a 5. The figure shown below represents a simplified model of ajet engine mounted to a a mechanism that acts as a spring of stiffness k and has moment of inertia J and mass m and that the rotation of the engine (ie. the vectoring of the engine) is related to the vertical displacement of the engine, x(t), by the radius, ro (i.e. xro0). Calculate the equation of motion, x(t) of this system as well compares the natural frequency of the system versus the percent that the spring oscillating mass. Use your plot to comment on when it is no longer appropriate to neglect the mass of the spring in as its natural frequency. Create a plot that mass is of the SS S modeling our Wing (ground) Mount, k, ms L X Engine, J, m

Answer 1

is enagy mi kinetic The Tping JA $2 T F kinetie energy in the Spring The ms X Tiny 3 Thus the total kinetic enegy J m 3 Just poential ugy The Lagrange ermulation, the equation ing the motien eult hom Ms J mt 92 , 2 2 dt 2t +. 2 3 K m+J 3/