im trying to make a m.file function in order to apply to underdamped systems
here is the 2nd ode
r" + 0.9214*r' + 9.2141 * r = -4.8202*dirac(t)
the answer should be -1.6066*exp(-0.4607 * t) * sin(3.0003*t)
but matlab returns this
-(24101*900185551^(1/2)*exp(-(4607*t)/10000)*sin((900185551^(1/2)*t)/10000)*sign(t))/900185551
here, 24101*900185551^(1/2)/900185551 is 0.8033 which is 1/2 of 1.6066
what did i miss?? and how can i shorten those long numbers?
here is the code
syms r(t)
dr = diff(r);
ode = diff(r,t,2) + 0.9214*diff(r,t) + 9.2141*r == -4.8202*dirac(t);
cond1 = r(0) ==0;
cond2 = dr(0) ==0;
conds = [cond1 cond2];
ySol(t) = dsolve(ode, conds);
ySol = simplify(ySol)
ySol(t) =
-(24101*900185551^(1/2)*exp(-(4607*t)/10000)*sin((900185551^(1/2)*t)/10000)*sign(t))/900185551
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