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linear time-invariant continuous system and Matlab

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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).

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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.