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linear time-invariant continuous system and Matlab

Please refer to attached. Please submit Matlab code along with plots and anwsers. Thanks.

A linear time-invariant continuous-time system has the impulse response below:
h(t) =[cos 2t + 4 sin 2t]u(t)

(a) Determine the transfer function H(s) of the system.
(b) Plot the system impulse response using MATLAB.
(c) The input, x(t) is defined as x(t) = 5/7e^-t - 12/7e^-8t. Find X(s).
(d) Compute the output response Y(s).
(e) Compute and plot (using Matlab) y(t).


Solution Summary

The solution is comprised of detailed explanation of application of Laplace transform to find the transfer function of the linear time-invariant continuous system in s-domain. It also shows the calculation of the impulse response of the system. Furthermore, it also elaborates on finding the system output in both s-domain and time domain with certain input. Finally, the application is verified in Matlab codes.