finding laplace transform of heaviside function
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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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Answers (1)
Walter Roberson
on 13 Dec 2018
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) )
Not sure what this has to do with laplace ?
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