Derive the transfer function, g(s), for the mechanical system provided below:

a) g(s) = (2s² + 3s + 5)
b) g(s) = (s³ + 2s² + s + 1)
c) g(s) = (3s³ + 2s² + 4s + 1)
d) g(s) = (4s² + s + 3)