A spring which is extended by an amount

x

has a tension

Kx

. A mass

M

is placed on the spring; gravity causes the spring to extend. The system starts with the spring extended by an amount

M(g)/(2)K

. After a long time the mass and spring reach a new equilibrium position. Given that the spring and its surroundings are at a temperature

T

, obtain an expression for the increase in the entropy of the universe.