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- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/17%3A_Second-Order_Differential_Equations/17.04%3A_Applications_of_Second-Order_Differential_EquationsScond-order linear differential equations are used to model many situations in physics and engineering. Here, we look at how this works for systems of an object with mass attached to a vertical spring...Scond-order linear differential equations are used to model many situations in physics and engineering. Here, we look at how this works for systems of an object with mass attached to a vertical spring and an electric circuit containing a resistor, an inductor, and a capacitor connected in series. Models such as these can be used to approximate other more complicated situations; e.g., bonds between atoms or molecules are often modeled as springs that vibrate.
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Differential_Equations_(No_Linear_Algebra_Required)/05%3A_Applications_of_Second_Order_Linear_Equations/5.01%3A_Applications_of_Second-Order_Differential_EquationsAccording to Hooke’s law, the restoring force of the spring is proportional to the displacement and acts in the opposite direction from the displacement, so the restoring force is given by \(−k(s+x).\...According to Hooke’s law, the restoring force of the spring is proportional to the displacement and acts in the opposite direction from the displacement, so the restoring force is given by −k(s+x). The spring constant is given in pounds per foot in the English system and in newtons per meter in the metric system.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_375%3A_Pre-Calculus/08%3A_Graphs_of_the_Trigonometric_Functions/8.04%3A_Sinusoidal_ModelsThis section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitud...This section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitude, period, phase shift, and vertical shift. It explains how these properties relate to physical concepts like frequency and angular frequency. Examples, such as modeling the height of a Ferris wheel rider over time, illustrate the application of these models in practical scenarios.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_373%3A_Trigonometry_for_Calculus/05%3A_Graphs_of_the_Trigonometric_Functions/5.04%3A_Sinusoidal_ModelsThis section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitud...This section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitude, period, phase shift, and vertical shift. It explains how these properties relate to physical concepts like frequency and angular frequency. Examples, such as modeling the height of a Ferris wheel rider over time, illustrate the application of these models in practical scenarios.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/08%3A_Graphs_of_the_Trigonometric_Functions/8.04%3A_Sinusoidal_ModelsThis section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitud...This section discusses building sinusoidal models using the sine function to represent real-world phenomena, such as wave patterns. It covers key properties of sinusoidal functions, including amplitude, period, phase shift, and vertical shift. It explains how these properties relate to physical concepts like frequency and angular frequency. Examples, such as modeling the height of a Ferris wheel rider over time, illustrate the application of these models in practical scenarios.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/17%3A_Second-Order_Differential_Equations/17.03%3A_Applications_of_Second-Order_Differential_EquationsScond-order linear differential equations are used to model many situations in physics and engineering. Here, we look at how this works for systems of an object with mass attached to a vertical spring...Scond-order linear differential equations are used to model many situations in physics and engineering. Here, we look at how this works for systems of an object with mass attached to a vertical spring and an electric circuit containing a resistor, an inductor, and a capacitor connected in series. Models such as these can be used to approximate other more complicated situations; e.g., bonds between atoms or molecules are often modeled as springs that vibrate.