Suppose that a new gym is looking to rent one floor from a 5-storey building (ground floor = floor 0, and then there are upper floors 1 - 5). The building has floors 1, 2 and 3 available to lease. Each floor of the building is 5 metres apart. The owner of the building has studied as a civil engineer and is concerned that the vibrations on the support beams caused by heavy weights being dropped will disturb the other tenants. After some experiments by dropping objects of varying weights, the building owner concluded that the average deviation of a support beam from the vertical is 0.0033 radians. Please provide full steps, thanks in advance.
(a) Calculate the horizontal displacement of the support beam on the ground floor when a weight is dropped on (i) floor 1 (ii) floor 2 (iii) floor 3.
(b) Calculate the horizontal displacement of the support beam on the fifth floor when a weight is dropped on (i) floor 1 (ii) floor 2 (iii) floor 3.
(c) Comment on which floor should be leased by the gym to minimise the horizontal displacement of the support beams for the building; include your reasons for choosing that floor.