Problem $1$

Implement the following system:

d

x

d

t

$=$

y

d

y

d

t

$=$

x

$$

x

$3$

$$

$0\mathrm{.}25$

y

$+$

A

sin

$($

t

$)$

t

$(1)$

$(2)$

a$)$ Run for t $=100$ with A $=0\mathrm{.}2645,$ x $=0\mathrm{.}9,$ y $=0\mathrm{.}4.$

b$)$ Run for t $=500$ with A $=0\mathrm{.}2645,$ x $=0\mathrm{.}9,$ y $=0\mathrm{.}4.$

c$)$ Find two other sets of conditions that give different dynamcis to those in a and b$.$

d$)$ Describe your observations.