Pin p is constrained to move along the curve defined by the lemniscate r=(4sin2θ)ft.if the slotted arm oa rotates counterclockwise with a constant angular velocity of θ˙ = 1.0 rad/s , determine the magnitude of the velocity of peg p when θ = 59 ∘.

position of the peg is given by the equation

now the rate of change in position is given as

given that

now we have

so its speed will be 3.76 m/s in magnitude

First of all, looks like your teacher is indeed pretty horrible. Secondly, the constraints to consider would be proper weight distribution, methods to minimize excessive motion of the building structure, and quantities such as volume and density, which would help in determining the optimal structure. Keeping the frequency of oscillation for a building low in case of an earthquake or natural disaster would also be a priority.