How Newton’s Second Law Predicts the Rhythmic Motion of a Spring
In short: This video explains how to mathematically model simple harmonic motion using calculus. By applying Newton’s second law, you can derive the sinusoidal functions that describe an object's position, velocity, and acceleration over time.
Simple harmonic motion is represented by a second-order differential equation. Solving this equation yields a sinusoidal function that maps an object's position as it oscillates.
Because these functions are linked through calculus, differentiating the position function allows you to determine the object's velocity and acceleration at any given moment. These derived functions also exhibit sinusoidal behavior, illustrating the predictable, repeating nature of the system.
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Sources
- Summary by Intellect · source: Modeling spring-mass oscillators | AP Physics | Khan Academy
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