Consider the following graph of this coupled pendulum system:

Spring$-$Mass System

Fig. $1.$ The Coupled Pendulum System

Note that the two pendulums are coupled by a linear spring.

Under the assumption of small angular displacements, the dynamics of this system are captured by the coupled system of ordinary differential equations:

$\backslash$theta $1=\backslash$theta $1($m$1($L$1\backslash$theta $21$g$)$KL$1)+$KL$2\backslash$theta $2$m$1$L$1\backslash$theta $2=\backslash$theta $2($m$2($L$2\backslash$theta $22$g$)$KL$2)+$KL$1\backslash$theta $1$m$2$L$2$

where:

m$1$ is the mass of the first point mass

m$2$ is the mass of the second point mass

L$1$ is the length of the first pendulum

L$2$ is the length of the second pendulum

$\backslash$theta $1$ is the angular position of the first pendulum

$\backslash$theta $2$ is the angular position of the second pendulum

g is acceleration due to gravity

K is the Hooke's Law spring constant for the spring

Note that we are also going to work with the following variables:

t$0$ is the initial time

tf is the final time

$\backslash$Delta t is the time step

$\backslash$Delta R is the relative tolerance

$\backslash$Delta A is the absolute tolerance

You are a junior engineer working for an engineering firm. Your manager asks you to create a GUI, though fortunately you took CMPSC $200$ at Penn State and you have all of the knowledge that you would need to deliver the GUI. Per your manager's specifications, your GUI must meet the following design criteria:

Using GUIDE, create a layout reasonably similar to the layout provided in Figs. $2$ and $3.$ Make sure to adjust the text displayed by the panel, static textboxes, edit textboxes, and pushbuttons to match that displayed $($or not displayed, in the case of the edit textboxes$)$ in Fig. $2.$ In particular, your GUI layout should contain:

$4$ edit textboxes $($to allow the user to enter values for $\backslash$theta $1(0)($in deg$),\backslash$theta $1(0)($in deg$/$sec$),\backslash$theta $2($in deg$),$ and $\backslash$theta $2(0)($in deg$/$sec$)).$

$4$ static textboxes $($to serve as labels for the edit textboxes described in the previous sub$-$bullet$)$

A panel $($to group together the edit and static textboxes noted in the previous two sub$-$bullets$)$

$2$ push buttons $$ one to activate the graph of the plot, and one to reset the graph

An axis $($to depict the plot$)$