Problem

A box of mass 0.75 kg is thrown on a scale, causing both the scale and the box to move ver...

A box of mass 0.75 kg is thrown on a scale, causing both the scale and the box to move vertically downward with an initial speed of 0.5 m/s. Before the box lands on the scale, the scale is in equilibrium. The total mass of the scale’s moving platform and the box is m = 1.25 kg. Modeling the platform’s support as a spring and dashpot with stiffness k = 1000 N/m and damping coefficient c = 70.7 N·s/m, find the response of the scale. Hint: Place the origin of the y axis at the position of the platform corresponding to the equilibrium configuration of the platform and box together.