Question

determine a transformada inversa de laplace de F(S) = k/s^2(s^2+k^2)

Answer 1

$\dfrac{k}{s^2(s^2+k^2)}=\dfrac{A}{s^2}+\dfrac{B}{s^2+k^2}\\\\As^2+Ak^2+Bs^2=k\\\\ \left \{ {{A+B=0} \atop {Ak^2=k}} \right.\\\\A=\dfrac{1}{k},\ B=-\dfrac{1}{k}\\\\\dfrac1k\cdot\dfrac{1}{s^2}-\dfrac1k\cdot\dfrac{1}{s^2+k^2}\\\\\\\mathcal{L}^{-1}\{\dfrac{k}{s^2(s^2+k^2)}\}=\dfrac tk-\dfrac{\sin (kt)}{k^2}=\dfrac{kt-\sin(kt)}{k^2}$

Answer 2

Resposta:

Explicação passo-a-passo: