Integrated Maths 10+

What are the features of a cycle?

Cyclic behavior is something that occurs in a repeating pattern and goes around continuously. This behavior can be seen throughout many aspects of our environment. Some examples include; seasons, ferris wheels, moon cycle, menstruation cycle, cycle of violence, water cycle, cell cycle, your daily life cycle and even the cycle performed when buying products.
Not all cyclic behaviors are visible but in fact, there are many intangible cycles in this world. The cell cycle is a great example of an intangible cycle because we cannot see cells as they are too small to be apparent. Thus, it is impossible for humans to watch the process of cell division because it is tiny and its taking place within our body. The water cycle is observable except when it is going through the process of condensation (when the water vapor becomes cool and reshape into water droplets). Water vapor is invisible and this action is taking place at a very high altitude thus, intangible. 

The common features of cycles are repetition, periodicity and amplitudes. Like the ferris wheel and moon cycle, the cycle will continue to keep on repeating. After a ferris wheel makes a complete round, it will immediately begin its cycle again. The periodicity of cyclic behavior is the duration of one complete cycle in a repeating process. The moon cycle’s period is the duration from which the moon is a new moon and completes a full cycle until it’s a new moon again. The amplitude can be defined as the distance from the middle line to the maximum or minimum point of a cycle’s graph.

Cycles vary from their starting point, amplitudes, time taken to complete a full cycle (periods/frequencies), simple or complicated stages, amplitudes, and the end points. As I have mentioned earlier, the moon cycle has its own distinctive cycle. It’s ‘starting point’ is the new moon and ‘end point’ is the waning crescent, which is when the cycle has completed its full event. Depending on the cycle, they each have different periods/frequencies. The moon cycle’s period is the duration it takes for the new moon to complete its cycle and become a new moon again. The period of a cell cycle is once it reaches cell division but for the period of a ferris wheel, it is when a specific cabin makes a complete round. Within these examples, we can see they all vary in the duration it takes for each to complete one full cycle. The periodicity of a moon cycle will most likely take a longer to complete than the cycle of a ferris wheel.
Cycles can be measured by looking at the periods/frequencies and the amplitudes. By looking at the periods, we can measure the overall time it takes to complete a full cycle of that event. Amplitudes enable us to measure the magnitude of change in the cycle and locate it’s highest peak (maximum) and lowest point (minimum) of the cycle.
We will need to mathematically model the behavior of the ferris wheel by looking at it’s amplitude and periods. We will need to model this behavior of the ferris wheel to help inform people how long the overall ride will take and interest costumers with the great height it is able to reach. The amplitude enables us to measure specific locations the cabin will be at a set time. But the accuracy of modelling the ferris wheel is unnecessary because many people are not overly worried about the time and in fact loose track of time as they are focused on the scenery. In comparison, its necessary for the moon cycle because modelling it will help us know the date of the month and help women know ahead of time the start of their menstrual cycle. 
Cyclic and trig behaviors are very significant in our world because they are everywhere! The cycle of the seasons is an example that can cause problems with the growth in crops and certain species lives, if it’s interrupted. I feel the menstrual cycle is most important in life because it’s an important process for women to be able to give birth. It’s also important for many teenagers to be educated about this cycle to not experience unintended pregnancies, which may alter the rest of their life.


One thought on “What are the features of a cycle?

  1. Yurika
    You have given good depth of thought to the features that cycles share and why we need to measure them. You have made good use of diagrams to explain cycles. (You could do with more though really – you have one image of an example, and the other image explains cycles.)
    Generally, though, this is a good, thoughtful post and it is pleasing to see your depth of thought here. More detailed feedback and your level of achievement will be posted on Moodle and Powerschool by early next week.

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