Problem on motion of the system

(a) A plane moving at a constant velocity, V, crashes into a building as shown in figure below. Due to the design against plane crash of that building, neither major damage nor explosion occurs but the building vibrates after the crash. Assuming that the building can be modeled as a single degree of freedom system, derive the equation of motion of the system. Given that the plane and building become an entity after the crash, the mass of the plane is 10% of the mass of the building (m), the building has stiffness k and damping coefficient c. Determine the response of the building, u(t).

(b) You are given three options to modify the building as follows:

Option 1: Change m to 2m,
Option 2: Change c to 2c, and
Option 3: Change k to 2k.

Assess these three options and find the option that will produce the minimum reaction of the building.

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