A voltage vL(t) 5 cos(1000 n t) V appears across a 50-mH inductor, where n is

A voltage vL(t) ¼ 5 cos(1000 n t) V appears across a 50-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 iL(0) ¼ 0 A. Use MATLAB and symbolic variables to compute an expression for iL(t).On the same axes, plot iL(t) versus timefor n¼ 1, 2, 3, 4, and 5, over an appropriate time scale. On another set of axes, plot the amplitude of iL(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?