The landing-gear unit of an airplane is examined under drop test to ensure a safety and comfort landing, as shown in Figure 1(b). The vibration at the airplane body, x(t) due to the dropping height, h can be governed by the simplified equation: m + cx + kx = F(t) where m is the equivalent mass of the airplane, c and k are the damping and stiffness coefficients respectively of the landing-gear unit. x, i & are the displacement, velocity and acceleration of the mass respectively. F(t) = mg is the forcing function where g is the gravity coefficient (i.e. 9.81 m/s). Given the dropping height of the testing is h = 5.10 m, determine the impact velocity at ground and the total vibration, x(t) experienced by the airplane in this condition. 60000 i + 120000x + 3000000x = 60000g, x(0) = 0, x(0) = /2gh. Hint: Euler's Formula: etix = cosx t i(sinx). (8 marks) m Landing Landing Dropping gear unit height, h eecee eece