As part of a test to evaluate material properties, a weight of mass, m, is placed on an uncompressed material and released under gravity (from rest). The stiffness and damping properties of the material specimen are assumed to be represented by spring and damper model elements in parallel. The displacement, y, of the mass in the downward direction is measured using an available displacement non-contact sensor. (a) Formulate a 2nd order differential equation displacement of the mass, y, in the downward direction, making sure to take into account the effect of gravity (essential for the experiment to work). Let k and b be the equivalent stiffness and damping parameters of the material specimen.