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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/Red_Rocks_Community_College/MAT_2561_Differential_Equations_with_Engineering_Applications/08%3A_Laplace_Transforms/8.10%3A_Spring_Problems_Iabout spring--mass systems.
- https://math.libretexts.org/Under_Construction/Purgatory/Differential_Equations_and_Linear_Algebra_(Zook)/05%3A_Applications_of_Linear_Second_Order_Equations/5.01%3A_Spring_Problems_Iabout spring--mass systems.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/06%3A_Applications_of_Linear_Second_Order_Equations/6.01%3A_Spring_Problems_Iabout spring--mass systems.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/07%3A_Trigonometric_Identities_and_Equations/7.07%3A_Modeling_with_Trigonometric_EquationsMany natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model ...Many natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model an equation to reflect periodic behavior? First, we must collect and record data. We then find a function that resembles an observed pattern and alter the function to get adependable model. Here. we will take a deeper look at specific types of periodic behavior and model equations to fit data.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/06%3A_Applications_of_Linear_Second_Order_Equations/6.01%3A_Spring_Problems_IThroughout the this section we’ll consider spring–mass systems without damping. We’ll consider systems with damping in the next section. We first consider the case where the motion is also free.
- https://math.libretexts.org/Courses/Las_Positas_College/Math_39%3A_Trigonometry/02%3A_Periodic_Functions/2.7%3A_Modeling_with_Trigonometric_EquationsMany natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model ...Many natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model an equation to reflect periodic behavior? First, we must collect and record data. We then find a function that resembles an observed pattern and alter the function to get adependable model. Here. we will take a deeper look at specific types of periodic behavior and model equations to fit data.
- https://math.libretexts.org/Courses/Reedley_College/Differential_Equations_and_Linear_Algebra_(Zook)/11%3A_Applications_of_Linear_Second_Order_Equations/11.01%3A_Spring_Problems_IThroughout the this section we’ll consider spring–mass systems without damping. We’ll consider systems with damping in the next section. We first consider the case where the motion is also free.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_373%3A_Trigonometry_for_Calculus/05%3A_Graphs_of_the_Trigonometric_Functions/5.05%3A_Harmonic_MotionThis section explains harmonic motion, focusing on simple harmonic motion (undamped) and damped harmonic motion. It describes the mathematical models for both types, detailing the use of sinusoidal fu...This section explains harmonic motion, focusing on simple harmonic motion (undamped) and damped harmonic motion. It describes the mathematical models for both types, detailing the use of sinusoidal functions to represent simple harmonic motion and quasi-sinusoidal functions with exponential damping factors for damped harmonic motion. The section includes practical examples and interactive elements to illustrate the concepts, showing the effects of different damping factors on motion.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/10%3A_Graphs_of_the_Trigonometric_Functions/10.05%3A_Harmonic_MotionThis section explains harmonic motion, focusing on simple harmonic motion (undamped) and damped harmonic motion. It describes the mathematical models for both types, detailing the use of sinusoidal fu...This section explains harmonic motion, focusing on simple harmonic motion (undamped) and damped harmonic motion. It describes the mathematical models for both types, detailing the use of sinusoidal functions to represent simple harmonic motion and quasi-sinusoidal functions with exponential damping factors for damped harmonic motion. The section includes practical examples and interactive elements to illustrate the concepts, showing the effects of different damping factors on motion.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.06%3A_Modeling_with_Trigonometric_EquationsMany natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model ...Many natural phenomena are also periodic. For example, the phases of the moon have a period of approximately 28 days, and birds know to fly south at about the same time each year. So how can we model an equation to reflect periodic behavior? First, we must collect and record data. We then find a function that resembles an observed pattern and alter the function to get adependable model. Here. we will take a deeper look at specific types of periodic behavior and model equations to fit data.
