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let's explore how we could use AI to analyze Let's denote:
and understand the swinging motion
described in the anecdote: •A as the amplitude
(m a xim um
- Data Collection: The AI tool could be displacement

equipped with sensors or cameras to capture the from the equilibrium
swinging motion accurately. These sensors position),
could track the position and velocity of the •ω as the angular
swing over time. frequency (related
to the period of
- Pattern Recognition: Once the data is collected, the oscillation), and
AI tool could use pattern recognition algorithms to •t as the time.
identify the periodic nature of the swinging The function for
motion. It could recognize that the swinging the vertical
motion follows a sinusoidal pattern. motion of the
swing, assuming it starts from its highest point
- Mathematical Modeling: Using the data at t=0, can be represented as:
collected, the AI tool could then fit a mathematical y(t)=A.sin(ωt)
model to describe the swinging motion. This
model could involve sine and cosine functions to Similarly, the function for the horizontal motion,
accurately represent the vertical and horizontal assuming the swing moves horizontally as it
components of the swing, respectively. swings, can be represented as:
x(t)=A.cos(ωt)
- Prediction: With the mathe-
matical model in place, the These functions describe how the
AI tool could predict future height and horizontal position
positions of the swing of the swing change over time
based on its current as it oscillates back and forth.
state. It could estimate The amplitude A determines the
how high the swing will maximum height or displacement,
go with each subsequent while ω affects the speed and
swing and how far it will period of the swing's motion.
travel horizontally.

- Visualization: Finally, Therefore, the collaboration
the AI tool could generate between AI and mathematical
visualizations to illustrate the predicted science offers unprecedented opportunities for
swinging trajectory. These visualizations utilizing mathematical principles to
could help users better solve real-world problems. This
understand the behavior of Navpreet Kaur synergy promises transformative
the swing and how it relates advancements with
TGT Maths,
to the mathematical N.k Bagrodia far-reaching implications
functions used to model it. Global School for science and technology.

36 xÉ<Ç =cÉxÉ ekpZ -2024