Find the transfer function $\frac{Y(s)}{F(s)}$ of the following mechanical system.

Select one:

a$.\frac{Y(s)}{F(s)}=\frac{1}{m{s}^2+bs+\frac{k}{2}}$

b$.\frac{Y(s)}{F(s)}=\frac{1}{m{s}^2+bs+k}$

c$.\frac{Y(s)}{F(s)}=\frac{1}{m{s}^2+bs+2k}$

d$.$ None of these

e$.\frac{Y(s)}{F(s)}=\frac{2}{m{s}^2+bs+k}$