
(c) Find the general solution for P
k
, k ¼1, 2, 3, . . . when
(i) d
k
¼
0, k ¼ 0
D, k ¼ 1, 2, 3, ...
(ii) d
k
¼
0, k ¼ 0, 2, 4, ...
D, k ¼ 1, 3, 5, ...
(iii) d
k
¼
0, k ¼ 0
2D, k ¼ 1, 3, 5, ...
D, k ¼ 2, 4, 6, ...
(
4.68 Figure E4.68 shows the relationship between acceleration, velocity, and position of a particle
moving along a straight line.
A(s) V(s) X(s)
1
s
1
s
0
t
v(t)=
∫
a(t΄) dt΄
0
t
x(t)=
∫
ν(t΄) dt΄
FIGURE E4.68
(a) Write the differential equations relating v(t) and a(t), x(t) and v(t), and x(t) and a(t).
(b) Use trapezoidal integration to approximate the three differential equations. That is, find
the difference equations relating v
k
and a
k
, x
k
and v
k
, and x
k
and a
k