Damped Harmonic Oscillator
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Differential Equations
This example demonstrates solutions to a mass-spring-shock absorber system based on second-order differential equations with constant coefficients. It involves core mathematical concepts like differential equations, vibration theory, damping effects, and parameter variations. The construction uses commands like Point, If, and objects such as k, V0, b, m, alpha2, alpha1, X0, A_3, m2a, m1a, A_1, B_1, text elements, and sliders for interactive exploration. Suitable for high school and above students learning about physical vibration systems and mathematical modeling.
GeoGebra Commands & Parameters
Point(yAxis) → V0Point(yAxis) → X0If(b^(2) > ((4 * m) * k), h''(x), If[b^(2) ≟ ((4 * m) * k), g''(x), f''(x)]) → accIf(m ≟ 0, p'(x), If[b^(2) > ((4 * m) * k), h'(x), If[b^(2) ≟ ((4 * m) * k), g'(x), f'(x)]]) → v