(Solved): A large robotic arm can be modeled by the circuit below on the left. When a voltage is applied to t ...

A large robotic arm can be modeled by the circuit below on the left. When a voltage is applied to the input, the voltage across the $1\mathrm{k}\Omega$ resistance will determine how far the arm will move. (Notice: the voltage source must be included in the model for all time for this system to work at all - the drawing on the left was just for reference). For every $0.1\mathrm{V}$ applied at the output, the arm will move 1 inch. Unfortunately, the $100\Omega$ resistor creates a voltage divider which means that only a fraction of the input voltage gets applied to the output. The system's inherent (meaning unintended) $0.5\mathrm{F}$ capacitance prevents the arm from moving instantaneously. Determine the output response of the $\mathrm{RC}$ circuit (both the equation and graph) to a $5\mathrm{V}$ step function (leading edge of a square wave). From your work, determine how far the arm will move if $5\mathrm{V}$ are applied at the input. Also determine how long it will take before the arm arrives at its final destination.