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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 38 "  maple solve of ODE for mountain bike" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 32 "clear workspace & load ODE stuff" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 10 "define ODE" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 73 "ode := diff(u(t),t,t) + b*diff(u(t),t)+ c*u(t) = -A*o
mega^2*sin(omega*t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 16 "solve without IV" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "soln := dsolve([ode],u(t));" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "extract solution into u
seful form" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "u(t) := subs(soln,u(t
));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 19 "calculate amplitude" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "a1 := coeff(u(t),'cos(omega*t)',1);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 35 "a2 := coeff(u(t),'sin(omega*t)',1);" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 44 "sqrt(a1^2 + a2^2); amplitude := simplify(%);
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