After applying the Laplace transform onto a differential equation that models a vibrating problem,the following Laplace function was obtained: f(s)=\frac{s^{2}+2 s+3}{(s+1-i)(s+1+i)(s+1-2 i)(s+1+2 i)} 1- Knowing that the roots are imaginary

for both equations, we can write the equation in thefollowing form \frac{s^{2}+2 s+3}{(s+1-i)(s+1+i)(s+1-2 i)(s+1+2 i)} =\frac{A}{(s+1-i)}+\frac{B}{(s+1+i)}+\frac{C}{(s+1-2 i)}+\frac{D}{(s+1+2 i)} Multiply the previously given brackets and Show the found equations 0. s³ + s? + 2s' + 3s° = (-1 –)s³ + (-2–)s² + (-3 –)s + (-4 –)s° Multiply the previously given brackets and Show the found equations 0 . s^{3}+s^{2}+2 s^{1}+3 s^{0}=(-1-) s^{3}+(-2-) s^{2}+(-3-) s+(-4-) s^{0} Solve the 4 equations with the 4 unknowns