3a: Build a mathematical model and analytically solve the resulting differential equation. The simplified robotic tail system can be modeled according to the diagram below. Here, we have abstracted away the wheeled robot and represented it as a rigid wall, with a tail connected to it via a hinge joint. For our purposes, we've also chosen the robotic tail to be a passive dynamic system, meaning that its behavior is governed by 0th, 1st, and 2nd order elements (spring, damper, and inertia, respectively). The tail has been reduced to a point mass at a distance from the center of the tail's rotation, such that the tail's inertia is = 2 . The rotational spring-damper has spring constant and damping constant . The spring produces zero torque at = 0. All perturbations to the robot are represented by an external torque acting on the system. For this problem, we can ignore the effects of gravity on the mass. Your first task is to find the differential equation that models this system when there is no external torque acting on the tail ( = 0). For this first pass, let's say = 0.4 , = 0.5 , = 0.3 , and =