The speed of the baby can be determined by using the total mechanical energy of the system: the energy at the streched position equals the energy at equilibrium.

So, if we let x=0 be at equilibrium, then the energy at equilibrium would be:

E = (1/2)k(0)^2 + (1/2)mv^2

where k is the string constant, m is the mass (10kg) and v is the speed.

when the baby is released, it is a distance 0.45m from equilibrium and at rest, so

E = (1/2)k(0.45m)^2 + (1/2)m(0)^2