The IVP for a mass-spring-dashpot system is                 where (0) =  and  ’(0) = . In this problem  are given numbers and ( ) is a given forcing function. (a) Using finite difference...

The IVP for a mass-spring-dashpot system is

where
(0) =
 and
 ’(0) =
. In this problem
 are given numbers and
() is a given forcing function.

(a) Using finite difference approximations for
” and
’, derive a finite difference approximation for the differential equation that has truncation error that is
(
²).

(b) Convert the initial conditions so they apply to the finite difference approximation. Your approximation of
y
’(0) =
 must have a truncation error that is
(
²).

(c) Setting
 =
‘, find a first-order system for
 and
.

(d) Write down a numerical method for solving the problem in part (c) that has a truncation error that is
(
²).