finding laplace transform of heaviside function

Question

Brenda Galabe 2018-12-13

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/435492-finding-laplace-transform-of-heaviside-function

回答： Walter Roberson 2018-12-13

在 MATLAB Online 中打开

trying to get lapace and plot :

θ” + 2θ′ + 6θ = [H(t) − H(t − 1)],

θ(0) = 4, θ′ (0) = 5,

H is the Heaviside function defined by

H(t) = { 0, x < 0, 1, x ≥ 0.

Find and sketch θ(t).

my code : error with dsolve

laplace('heaviside(t)-heaviside(t-1)',t,s)
syms t theta gensoln initsoln
eq = 'D2theta + 2*Dtheta + 6*theta -heaviside(t)+heaviside(t-1)'
initsoln = dsolve(deq,'theta(0)=6, Dtheta(0)=6', 't')
pretty(initsoln)

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Brenda Galabe 2018-12-13

other differential like these worked just as is the only thing that was changed is theta

Brenda Galabe 2018-12-13

i think i got got it suppose to be dsolve(eq) not dsolve(deq)

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Answer 1

Walter Roberson 2018-12-13

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/435492-finding-laplace-transform-of-heaviside-function#answer_352104

在 MATLAB Online 中打开

sympref('HeavisideAtOrigin',1);      %needs R2015a or later
syms s t
expr1 = heaviside(t)-heaviside(t-1);
expr2 = laplace(expr1, t, s)       %not sure why we are doing this  ??
syms theta(t)
Dtheta = diff(theta);
D2theta = diff(Dtheta);
deq = D2theta + 2*Dtheta + 6*theta == expr1;
initsoln = simplify( dsolve(deq, theta(0)==6, Dtheta(0)==6, t) )