Figure Q4 shows an aeroplane approaching a runaway for landing. The aeroplane consists of front and rear landing gear set which have different stiffness values. The front landing gear set has stiffness coefficient value, k, = 6T0 kN/m while the rear landing gear set has stiffness coefficient value, k, = 7U0 kN/m. The distance of each landing gear to the center of gravity is l, = 9 m and l2 = 2.5 m respectively. The mass of the aeroplane is given as m = 10,000 kg while the radius of gyration, rg = 2 m. By neglecting the damping coefficient of the landing gear: Note: The values of T and U depend on the respective 5th and 6th digits of your matric number as the following number format AD PQRSTU. For example, if your matric number is AD170154 gives the value of T = 5 and U = 4, thus stiffness coefficient value k,= 650 kN/m and k2= 740 kN/m. (a) Illustrate the problem as mass-spring system. (b) Construct the equation of motion, complete with all values in the matrix form (c) Evaluate the natural frequencies of the system. (d) Estimate the mode shape of the system, complete with its mode shape diagram.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.