Solve for \( v_{2} \) \[ \frac{\left(v_{1}-v_{2}\right) w}{4}=s \]

To solve for \( v_{2} \) from the equation \[ \frac{(v_{1} - v_{2}) w}{4} = s, \] we first multiply both sides by 4 to eliminate the fraction: \[ (v_{1} - v_{2}) w = 4s. \] Next, we divide both sides by \( w \) (assuming \( w \neq 0 \)): \[ v_{1} - v_{2} = \frac{4s}{w}. \] Now, isolating \( v_{2} \) involves rearranging the equation: \[ -v_{2} = \frac{4s}{w} - v_{1}. \] Multiplying through by -1 gives: \[ v_{2} = v_{1} - \frac{4s}{w}. \] Thus, the solution for \( v_{2} \) is: \[ v_{2} = v_{1} - \frac{4s}{w}. \]