$6)$ Answer the following:

a$)$ For the circuit shown in Figure $6$ below, determine the numerical value of $\backslash (\backslash$alpha $\backslash )$ such that the time constant $\backslash (\backslash$tau $\backslash )$ for the $\backslash ($ t$>0\backslash )$ circuit is $40$ ms $.$ Verify your answer to this part in LTSpice, which should agree very well.

b$)$ Using the numerical $\backslash (\backslash$alpha $\backslash )$ found in part $($a$),$ find $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$x$\}\}($t$)\backslash )$ for $\backslash ($ t$>0\backslash )$ and sketch the response; list the equation, show the sketch, label the plot axes, and otherwise make your sketch neat$-$looking and easy to comprehend. Show your by$-$hand work, and show your verification results from LTSpice and Matlab. The by$-$hand and simulated results should agree very well.

Figure $6.$ Circuit for Problem $6.$