A voltage \(v_{\mathrm{L}}(t)=5 \cos (1000 n t) \mathrm{V}\) appears across a \(50-\mathrm{mH}\) inductor, where \(n\) is a positive integer that controls the frequency of the input signal. The amplitude of the input signal is constant. Assume \(i_{\mathrm{L}}(\mathrm{O})=0 \mathrm{~A}\). Use MATLAB and symbolic variables to compute an expression for \(i_{\mathrm{L}}(t)\). On the same axes, plot \(i_{\mathrm{L}}(t)\) versus time for \(n=1,2,3,4\), and 5 , over an appropriate time scale. On another set of axes, plot the amplitude of \(i_{\mathrm{L}}(t)\) versus the coefficient \(n\).As \(n\) approaches infinity, what happens to the amplitude of the current? What type of circuit element does the inductor behave like as \(n\) approaches infinity?