We now consider $C$ as a function of $.$ We use again ${}_0=3,c=2$ and $y(0)=y^{\text{'}}(0)=0.$

The previous problem determined $C$ for a specific value of $.$ Here we consider a range

of values for $$ and determine numerically the corresponding amplitude $C.$ We then plot

the result as a function of $,$ together with the theoretical amplitude from $(3).$ The plot

is shown in Figure $2.$ You may need the following MATLAB program.

LAB$06$ex$2$

clear all; $\%$this deletes all variables

omega$0=3$;$c=2$;

OMEGA $=1$:$0\mathrm{.}01$:$4$;

OMEGA$))$;

Ctheory OMEGA$))$;

$t0=0$;$y0=0$;$v0=0$;$Y0=[y0$;$v0]$;$tf=40$;$t1=13$;

for $k=1$: length $($OMEGA$)$

omega $=$ OMEGA $(k)$;

param omega$0,$ c$,$omega$]$;

$,$ param