(Solved): Consider the diagram of the solenoid shown below and the simplified differential equation attemptin ...

Consider the diagram of the solenoid shown below and the simplified differential equation attempting to describe its motion. Answer the following questions. \[ m \frac{d^{2} x(t)}{d t^{2}}+D \frac{d x(t)}{d t}-K i(t)=0 \] Explain the physical significance of the terms used \( I_{\text {in }} \) the equation. Express the above response as a transfer function of the form \[ Q(s)=\frac{x(s)}{i(s)} \] in Laplace space. Use the Final Value Theorem to demonstrate the system is unstable following a unit step-input function of 1 ampere. Explain your reasoning. How might you change the system to make it stable and better model the solenoid shown?