A pendulum $($Figure $1)$ is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth.

As a software engineer, you are required to design and develop a multi$-$layer, object$-$oriented analysis and design using Unified Modelling Language $($UML$).$ A pendulum system consists of a potentiometer fitted to the mechanical system as shown in Figure $1.$ The user is provided with a Graphical User Interface as illustrated in Figure $2.$ When the user chooses "start" by pressing the "Acquire$/$Stop$"$ button, the program captures the motion of the pendulum. When the user swings the pendulum bob, the microcontroller captures the output voltage of swings

and sends it to a PC via USB port $($serial communication$).$ This is continuous until the user chooses "stop" by pressing the "Acquire$/$Stop$"$ button. Then, the program saves the data. When the user chooses "display the motion", the program plots the angle as well as the $x$ and $y$ motion coordinates of the pendulum. When the user chooses "calculate", the program displays the period and frequency as well as the maximum amplitude.

Figure $2$

$($a$)$ Plan and propose a software architecture solution for the system. Use conceptual sketching to visualize the architecture consisting of Tier $1,$ Tier $2$ and Tier $3.$

$[20$ Marks$]C5$

$($b$)$ The use$-$case diagram is the dynamic diagram to represent interaction behavior between the users and the "use$-$cases". Develop a use$-$case diagram for the system.

$[20$ Marks$]C5$

$($c$)$ Based on the proposed solution in $($a$),$ formulate the class diagram for Tier $1$ and Tier $2$ of the system.

$[20$ Marks$]$

$C5$

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