Page 237 -

220 5. Some worked examples arising from physical problems

We introduce

and then the equation for becomes

We seek a solution, periodic in T and bounded in in the familiar form

and so obtain

and so on. The initial conditions give

The general solution for from (5.61a), is

for arbitrary functions and the initial conditions, (5.62a,c), require that

and so we select

Equation (5.61b) then becomes

where is periodic in T, i.e. in only if