Use MATLAB to solve the IVP using Laplace Transformation(1500points) IVP: Note t

Question

Use MATLAB to solve the IVP using Laplace Transformation(1500points)

IVP:

Note that g (t) is a piecewise-defined function. In engineering one frequently encounters functions that are "off' or "on". For example, an external force acting on a mechanical system or a voltage impressed on a circuit can be turned off after a period of time. It is convenient to define a special function that is the number 0 (off) up to a certain time t = a and then the number 1 (on) after that time. This function is called the unit step function or the Heaviside function. The unit step function u(t - a) = 0, 0 get

Explanation / Answer

%Consider the initial value problem

%y'' + 2 y' + 2 y = g(t) , y(0) = 0 , y'(0) = 0

%with the right-hand side function

%g(t) = sint     for 0< t<pi
%g(t) = 0 for t>pi

%Find the Laplace transform of y'(t) : Y1 = s Y - y(0)

%Find the Laplace transform of y''(t) : Y2 = s Y1 - y'(0)

%Set the Laplace transform of the left hand side minus the right hand side to zero and solve for Y:

%Find the inverse Laplace transform of the solution:

%Plot the solution: (use myplot if ezplot does not work)

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