Question: Calculating a limes value on making assumptions with assume(ing)


I solved the homogeneous differential equation of a damped oscillator ((D@@2)(x))(t)+d*(D(x))(t)+k^2*x(t) = A*sin(omega*t) with maple, the output is:

x(t) = _C1*exp((-(1/2)*d+(1/2)*sqrt(d^2-4*k^2))*t)+_C2*exp((-(1/2)*d-(1/2)*sqrt(d^2-4*k^2))*t)

Now, as there is damping, the limit for t->infinity shoud be 0. I substituted:

hommod := subs(d^2-4*k^2 = Delta, rhs(l_hom))

 Then, I tried the limit(hommod, t = infinity) command for the three cases

assume(d > 0, k > 0, Delta < 0)

assume(d > 0, k > 0, Delta = 0)

assume(d > 0, k > 0, Delta > 0, Delta^2 < d)

(the assume command put before the limit-command every time). On Maple 11, the first two returned zero, but the last one did not compute. As we are doing a project, I know that Maple 9.5 returned different results (worse, chiefly), and even on my own machine I had different results with the same code. I also tried other variations, such as assuming Delta::positive etc., but neither of them was completely right. Who can help me?


Alexander Erlich


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