Proceed as in Example 4 in Section 11.3 to find a particular solution

x_p(t)

of equation (11) in Section 11.3

m

d²x

dt²

+ kx = f(t) (11)

when

m =

1

2

, k = 16,

and the driving force

f(t)

is as given. Assume that when

f(t)

is extended to the negative t-axis in a periodic manner, the resulting function is even.

f(t) = 2t t²,

0 < t < 2;