What is the inverse Laplace transform of this?

68 Views Asked by At

Can you give me a hand with this inverse Laplace transform?

$$H(s) = \frac{s^2 + 10^{12}}{s^2 + s\cdot10^6 + 10^{12}}$$

It is the transfer function of an RLC series circuit and $Vo(s) = VL(s) + VC(s)$.

1

There are 1 best solutions below

0
On

Thank you all for the tip's.

I finally choose the @Moo advice.

H(s) = 1 - (s+0.5*10^6) / ((s+0.5*10^6)^2 + 0.75*10^12) + (0.5*10^6) / ((s+0.5*10^6)^2 + 0.75*10^12)
h(t) = δ(t) + (0.5*10^6/0.75*10^12)* exp(-0.5^6*t)*sin(sqrt(0.75*10^12)*t) - 0.5*10^6*exp(-0.5^6*t)*cos(sqrt(0.75*10^12)*t)

It is correct? Thank you again. Juan.